Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
500 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722476 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#63471 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11720967 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11720871 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11720558 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C9×#823 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11720291 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10591012 | — | 3 | 1 | no | maximal |
| 9 | #10588426 | — | 3 | 1 | no | maximal |
| 10 | #88736 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C9×D12 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#3697 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3×Dic18 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | D3×#611 | — | 2 | 2 | no | — |
| 15 | #88646 | — | 2 | 1 | no | — |
| 16 | D9×D12 | — | 2 | 1 | no | — |
| 17 | #88639 | — | 2 | 1 | no | — |
| 18 | #88638 | — | 2 | 1 | no | — |
| 19 | C3×C9×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C4×C3⋊Dic9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C9×#208 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C3×#3664 | — | 2 | 1 | no | — |
| 23 | C3×Dic36 | — | 2 | 1 | no | — |
| 24 | (C2×D3)⋊Dic9 | — | 2 | 2 | no | — |
| 25 | #88418 | — | 2 | 1 | no | — |
| 26 | #88416 | — | 2 | 1 | no | — |
| 27 | #64307 | — | 3 | 1 | no | — |
| 28 | C3×#909 | — | 3 | 1 | no | — |
| 29 | #63863 | — | 3 | 1 | no | — |
| 30 | #63833 | — | 3 | 1 | no | — |
| 31 | #63710 | — | 3 | 1 | no | — |
| 32 | #63652 | — | 3 | 1 | no | — |
| 33 | C3×#823 | D3 | 1 | 1 | yes | characteristic |
| 34 | #63568 | — | 3 | 1 | no | — |
| 35 | #63498 | — | 3 | 1 | no | — |
| 36 | #63471 | — | 3 | 1 | no | — |
| 37 | #63471 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | C9×#100 | — | 3 | 1 | no | — |
| 39 | #63384 | — | 3 | 1 | no | — |
| 40 | #63384 | — | 3 | 1 | no | — |
| 41 | #63384 | — | 6 | 1 | no | — |
| 42 | C22×D3×C9 | D4 | 1 | 2 | yes | — |
| 43 | C2×D3×D9 | — | 2 | 2 | no | — |
| 44 | C2×C3×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 45 | #6233 | — | 2 | 1 | no | — |
| 46 | C2×C3⋊Dic9 | — | 2 | 1 | no | — |
| 47 | C4⋊(C3⋊D9) | D4 | 1 | 1 | yes | characteristic |
| 48 | C4×C3⋊D9 | — | 2 | 1 | no | — |
| 49 | #6226 | D4 | 1 | 1 | yes | characteristic |
| 50 | C3×#611 | — | 2 | 1 | no | — |
| 51 | C2×C3×Dic9 | — | 2 | 1 | no | — |
| 52 | C9×D12 | — | 2 | 1 | no | — |
| 53 | C9×D12 | — | 2 | 1 | no | — |
| 54 | C3×D36 | D4 | 1 | 1 | yes | characteristic |
| 55 | C3×C4×D9 | — | 2 | 1 | no | — |
| 56 | C3×Dic18 | — | 2 | 1 | no | — |
| 57 | C3×Dic18 | — | 2 | 1 | no | — |
| 58 | C3×Dic18 | D4 | 1 | 1 | yes | characteristic |
| 59 | #6195 | — | 2 | 2 | no | — |
| 60 | #6194 | — | 2 | 2 | no | — |
| 61 | D3×Dic9 | — | 2 | 2 | no | — |
| 62 | C3×C8×C9 | — | 2 | 1 | no | — |
| 63 | C9×C3⋊C8 | — | 2 | 1 | no | — |
| 64 | #5202 | — | 9 | 1 | no | — |
| 65 | #4746 | — | 9 | 1 | no | — |
| 66 | #3828 | — | 3 | 1 | no | — |
| 67 | C3×#235 | — | 3 | 1 | no | — |
| 68 | C2×C3×D12 | C2×D3 | 1 | 1 | yes | characteristic |
| 69 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 70 | D3×#67 | — | 6 | 2 | no | — |
| 71 | #3802 | — | 6 | 1 | no | — |
| 72 | D3×D12 | — | 6 | 1 | no | — |
| 73 | #3796 | — | 6 | 1 | no | — |
| 74 | #3795 | — | 6 | 1 | no | — |
| 75 | C32×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 76 | C4×C3⋊Dic3 | — | 3 | 1 | no | — |
| 77 | C3×#208 | C2×D3 | 1 | 1 | yes | characteristic |
| 78 | C3×Dic12 | — | 6 | 1 | no | — |
| 79 | C3×#204 | — | 6 | 1 | no | — |
| 80 | (C2×D3)⋊Dic3 | — | 6 | 2 | no | — |
| 81 | #3719 | — | 6 | 1 | no | — |
| 82 | #3717 | — | 6 | 1 | no | — |
| 83 | C2×D4×C9 | — | 3 | 1 | no | — |
| 84 | C2×#611 | — | 6 | 2 | no | — |
| 85 | #3699 | — | 6 | 1 | no | — |
| 86 | #3699 | — | 6 | 1 | no | — |
| 87 | D4×D9 | — | 6 | 1 | no | — |
| 88 | D4×D9 | — | 6 | 1 | no | — |
| 89 | #3697 | — | 3 | 1 | no | — |
| 90 | #3697 | — | 6 | 1 | no | — |
| 91 | #3697 | C2×D3 | 1 | 1 | yes | characteristic |
| 92 | C2×Dic18 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 93 | C9×M16 | — | 2 | 1 | no | — |
| 94 | C9×M16 | — | 3 | 1 | no | — |
| 95 | C9×M16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 96 | #3676 | — | 6 | 2 | no | — |
| 97 | C4×Dic9 | — | 3 | 1 | no | — |
| 98 | C4×Dic9 | — | 6 | 1 | no | — |
| 99 | #3664 | — | 2 | 1 | no | — |
| 100 | #3664 | — | 6 | 1 | no | — |
| 101 | Dic36 | — | 2 | 1 | no | — |
| 102 | Dic36 | — | 6 | 1 | no | — |
| 103 | C22×C3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×C3⋊D9 | — | 2 | 1 | no | — |
| 105 | C2×D3×C9 | — | 2 | 2 | no | — |
| 106 | C2×D3×C9 | — | 4 | 2 | no | — |
| 107 | C2×C3×D9 | — | 2 | 1 | no | — |
| 108 | D3×D9 | — | 8 | 2 | no | — |
| 109 | C3×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C3×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C3⋊Dic9 | — | 2 | 1 | no | — |
| 112 | C3⋊Dic9 | — | 4 | 1 | no | — |
| 113 | C3×Dic9 | — | 2 | 1 | no | — |
| 114 | C3×Dic9 | — | 4 | 1 | no | — |
| 115 | #1009 | — | 9 | 1 | no | — |
| 116 | #1004 | — | 9 | 1 | no | — |
| 117 | C3×#137 | — | 9 | 1 | no | — |
| 118 | #947 | — | 9 | 1 | no | — |
| 119 | #942 | — | 9 | 1 | no | — |
| 120 | #936 | — | 9 | 1 | no | — |
| 121 | #909 | — | 3 | 1 | no | — |
| 122 | #909 | — | 9 | 1 | no | — |
| 123 | C3×#100 | — | 3 | 1 | no | — |
| 124 | #837 | — | 9 | 1 | no | — |
| 125 | #825 | — | 9 | 1 | no | — |
| 126 | #825 | — | 9 | 1 | no | — |
| 127 | #825 | — | 9 | 1 | no | — |
| 128 | #825 | — | 18 | 1 | no | — |
| 129 | #823 | D9 | 1 | 1 | yes | characteristic, complemented |
| 130 | C22×C3×D3 | D12 | 1 | 2 | yes | — |
| 131 | C2×D32 | — | 6 | 2 | no | — |
| 132 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 133 | #638 | — | 6 | 1 | no | — |
| 134 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 135 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 136 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 137 | #634 | — | 3 | 1 | no | — |
| 138 | C3×#67 | — | 6 | 1 | no | — |
| 139 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 140 | C3×D12 | — | 2 | 1 | no | — |
| 141 | C3×D12 | — | 2 | 1 | no | — |
| 142 | C3×D12 | — | 3 | 1 | no | — |
| 143 | C3×C4×D3 | — | 6 | 1 | no | — |
| 144 | C3×Dic6 | — | 3 | 1 | no | — |
| 145 | C3×Dic6 | — | 6 | 1 | no | — |
| 146 | C3×Dic6 | — | 6 | 1 | no | — |
| 147 | #626 | — | 6 | 2 | no | — |
| 148 | #625 | — | 6 | 2 | no | — |
| 149 | D3×Dic3 | — | 6 | 2 | no | — |
| 150 | C23×C9 | — | 3 | 2 | no | — |
| 151 | C22×D9 | — | 6 | 2 | no | — |
| 152 | C32×C8 | — | 2 | 1 | no | — |
| 153 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 154 | D4×C9 | — | 6 | 1 | no | — |
| 155 | D4×C9 | — | 6 | 1 | no | — |
| 156 | C2×C4×C9 | — | 2 | 1 | no | — |
| 157 | C2×C4×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 158 | #611 | — | 2 | 1 | no | — |
| 159 | #611 | — | 6 | 2 | no | — |
| 160 | #611 | — | 6 | 2 | no | — |
| 161 | #611 | — | 6 | 1 | no | — |
| 162 | #611 | — | 12 | 1 | no | — |
| 163 | C2×Dic9 | — | 2 | 1 | no | — |
| 164 | C2×Dic9 | — | 6 | 2 | no | — |
| 165 | C2×Dic9 | — | 6 | 1 | no | — |
| 166 | C2×Dic9 | — | 12 | 1 | no | — |
| 167 | D36 | — | 3 | 1 | no | — |
| 168 | D36 | — | 6 | 1 | no | — |
| 169 | D36 | #67 | 1 | 1 | yes | characteristic |
| 170 | C4×D9 | — | 2 | 1 | no | — |
| 171 | C4×D9 | — | 6 | 1 | no | — |
| 172 | C4×D9 | — | 12 | 1 | no | — |
| 173 | Dic18 | — | 2 | 1 | no | — |
| 174 | Dic18 | — | 2 | 1 | no | — |
| 175 | Dic18 | — | 3 | 1 | no | — |
| 176 | Dic18 | — | 6 | 1 | no | — |
| 177 | Dic18 | #67 | 1 | 1 | yes | characteristic |
| 178 | C8×C9 | — | 2 | 1 | no | — |
| 179 | C8×C9 | — | 4 | 1 | no | — |
| 180 | C8×C9 | — | 6 | 1 | no | — |
| 181 | #455 | — | 27 | 1 | no | Sylow |
| 182 | C2×C3×C9 | — | 2 | 1 | no | — |
| 183 | C2×C3×C9 | #120 | 1 | 1 | yes | characteristic |
| 184 | C3⋊D9 | — | 4 | 1 | no | — |
| 185 | D3×C9 | — | 4 | 2 | no | — |
| 186 | C3×D9 | — | 4 | 1 | no | — |
| 187 | C3×#41 | — | 9 | 1 | no | — |
| 188 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 189 | C2×C3×D4 | — | 3 | 1 | no | — |
| 190 | C2×#67 | — | 18 | 2 | no | — |
| 191 | #239 | — | 18 | 1 | no | — |
| 192 | #237 | — | 18 | 1 | no | — |
| 193 | #237 | — | 18 | 1 | no | — |
| 194 | D3×D4 | — | 18 | 1 | no | — |
| 195 | D3×D4 | — | 18 | 1 | no | — |
| 196 | D3×D4 | — | 18 | 1 | no | — |
| 197 | D3×D4 | — | 18 | 2 | no | — |
| 198 | #235 | — | 3 | 1 | no | — |
| 199 | #235 | — | 9 | 1 | no | — |
| 200 | #235 | — | 9 | 1 | no | — |
| 201 | #235 | — | 18 | 1 | no | — |
| 202 | #235 | — | 18 | 1 | no | — |
| 203 | C2×D12 | — | 18 | 1 | no | — |
| 204 | C2×D12 | C2×D9 | 1 | 1 | yes | characteristic |
| 205 | C2×Dic6 | — | 3 | 1 | no | — |
| 206 | C3×Q16 | — | 18 | 1 | no | — |
| 207 | C3×SD16 | — | 18 | 1 | no | — |
| 208 | C3×M16 | — | 2 | 1 | no | — |
| 209 | C3×M16 | — | 3 | 1 | no | — |
| 210 | C3×M16 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 211 | C3×M16 | D32 | 1 | 1 | yes | characteristic |
| 212 | #217 | — | 18 | 2 | no | — |
| 213 | #216 | — | 18 | 1 | no | — |
| 214 | #215 | — | 18 | 1 | no | — |
| 215 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 216 | C4×Dic3 | — | 9 | 1 | no | — |
| 217 | C4×Dic3 | — | 9 | 1 | no | — |
| 218 | C4×Dic3 | — | 18 | 1 | no | — |
| 219 | #208 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 220 | Dic12 | — | 6 | 1 | no | — |
| 221 | Dic12 | — | 18 | 1 | no | — |
| 222 | #204 | — | 6 | 1 | no | — |
| 223 | #204 | — | 18 | 1 | no | — |
| 224 | C22×C32 | C2×D12 | 1 | 1 | yes | characteristic |
| 225 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 226 | C2×C3×D3 | — | 2 | 2 | no | — |
| 227 | C2×C3×D3 | — | 4 | 2 | no | — |
| 228 | C2×C3×D3 | — | 6 | 1 | no | — |
| 229 | D32 | — | 24 | 2 | no | — |
| 230 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 231 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 232 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 233 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 234 | C3×Dic3 | — | 6 | 1 | no | — |
| 235 | C3×Dic3 | — | 12 | 1 | no | — |
| 236 | C22×C9 | — | 2 | 1 | no | — |
| 237 | C22×C9 | — | 6 | 2 | no | — |
| 238 | C22×C9 | — | 12 | 2 | no | — |
| 239 | C22×C9 | D3×D4 | 1 | 1 | yes | characteristic |
| 240 | C2×D9 | — | 2 | 1 | no | — |
| 241 | C2×D9 | — | 6 | 1 | no | — |
| 242 | C2×D9 | — | 12 | 1 | no | — |
| 243 | C2×D9 | — | 24 | 2 | no | — |
| 244 | C4×C9 | — | 2 | 1 | no | — |
| 245 | C4×C9 | — | 2 | 1 | no | — |
| 246 | C4×C9 | D3×D4 | 1 | 1 | yes | characteristic |
| 247 | C4×C9 | C2×#67 | 1 | 1 | yes | characteristic |
| 248 | Dic9 | — | 2 | 1 | no | — |
| 249 | Dic9 | — | 4 | 1 | no | — |
| 250 | Dic9 | — | 6 | 1 | no | — |
| 251 | Dic9 | — | 12 | 1 | no | — |
| 252 | Dic9 | — | 12 | 1 | no | — |
| 253 | Dic9 | — | 12 | 2 | no | — |
| 254 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 255 | #137 | — | 9 | 1 | no | — |
| 256 | #137 | — | 27 | 1 | no | — |
| 257 | #124 | — | 27 | 1 | no | — |
| 258 | #104 | — | 27 | 1 | no | — |
| 259 | #104 | — | 27 | 1 | no | — |
| 260 | #100 | — | 3 | 1 | no | — |
| 261 | C3×C9 | #455 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 262 | C23×C3 | — | 3 | 2 | no | — |
| 263 | C22×D3 | — | 18 | 2 | no | — |
| 264 | C22×D3 | — | 18 | 2 | no | — |
| 265 | C22×D3 | D36 | 1 | 2 | yes | — |
| 266 | C3×Q8 | — | 9 | 1 | no | — |
| 267 | C3×Q8 | — | 18 | 1 | no | — |
| 268 | C3×Q8 | — | 18 | 1 | no | — |
| 269 | C3×D4 | — | 6 | 1 | no | — |
| 270 | C3×D4 | — | 6 | 1 | no | — |
| 271 | C3×D4 | — | 9 | 1 | no | — |
| 272 | C3×D4 | — | 18 | 1 | no | — |
| 273 | C2×C3×C4 | — | 2 | 1 | no | — |
| 274 | C2×C3×C4 | — | 18 | 1 | no | — |
| 275 | C2×C3×C4 | — | 18 | 1 | no | — |
| 276 | C2×C3×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 277 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 278 | #67 | — | 6 | 1 | no | — |
| 279 | #67 | — | 18 | 2 | no | — |
| 280 | #67 | — | 18 | 2 | no | — |
| 281 | #67 | — | 18 | 2 | no | — |
| 282 | #67 | — | 18 | 1 | no | — |
| 283 | #67 | — | 18 | 1 | no | — |
| 284 | #67 | — | 36 | 1 | no | — |
| 285 | C2×Dic3 | — | 6 | 1 | no | — |
| 286 | C2×Dic3 | — | 18 | 2 | no | — |
| 287 | C2×Dic3 | — | 18 | 1 | no | — |
| 288 | C2×Dic3 | — | 18 | 1 | no | — |
| 289 | C2×Dic3 | — | 36 | 1 | no | — |
| 290 | D12 | — | 2 | 1 | no | — |
| 291 | D12 | — | 2 | 1 | no | — |
| 292 | D12 | — | 3 | 1 | no | — |
| 293 | D12 | — | 9 | 1 | no | — |
| 294 | D12 | — | 9 | 1 | no | — |
| 295 | D12 | — | 18 | 1 | no | — |
| 296 | D12 | — | 18 | 2 | no | — |
| 297 | C4×D3 | — | 6 | 1 | no | — |
| 298 | C4×D3 | — | 18 | 2 | no | — |
| 299 | C4×D3 | — | 18 | 1 | no | — |
| 300 | C4×D3 | — | 18 | 1 | no | — |
| 301 | C4×D3 | — | 36 | 1 | no | — |
| 302 | Dic6 | — | 3 | 1 | no | — |
| 303 | Dic6 | — | 6 | 1 | no | — |
| 304 | Dic6 | — | 6 | 1 | no | — |
| 305 | Dic6 | — | 9 | 1 | no | — |
| 306 | Dic6 | — | 9 | 1 | no | — |
| 307 | Dic6 | — | 18 | 1 | no | — |
| 308 | C3×C8 | — | 2 | 1 | no | — |
| 309 | C3×C8 | — | 2 | 1 | no | — |
| 310 | C3×C8 | — | 4 | 1 | no | — |
| 311 | C3×C8 | — | 6 | 1 | no | — |
| 312 | C3⋊C8 | — | 2 | 1 | no | — |
| 313 | C2×C32 | — | 2 | 1 | no | — |
| 314 | C2×C32 | #882 | 1 | 1 | yes | characteristic |
| 315 | C3⋊D3 | — | 12 | 1 | no | — |
| 316 | C3×D3 | — | 4 | 2 | no | — |
| 317 | C3×D3 | — | 12 | 1 | no | — |
| 318 | C2×C9 | — | 2 | 1 | no | — |
| 319 | C2×C9 | — | 2 | 1 | no | — |
| 320 | C2×C9 | — | 4 | 1 | no | — |
| 321 | C2×C9 | — | 12 | 2 | no | — |
| 322 | C2×C9 | #937 | 1 | 1 | yes | characteristic |
| 323 | D9 | — | 4 | 1 | no | — |
| 324 | D9 | — | 12 | 1 | no | — |
| 325 | D9 | — | 24 | 1 | no | — |
| 326 | #41 | — | 9 | 1 | no | — |
| 327 | #41 | — | 27 | 1 | no | — |
| 328 | #41 | — | 54 | 1 | no | — |
| 329 | #41 | — | 54 | 1 | no | — |
| 330 | C2×Q8 | — | 9 | 1 | no | — |
| 331 | C2×D4 | — | 3 | 1 | no | — |
| 332 | C2×D4 | — | 54 | 1 | no | — |
| 333 | C2×D4 | — | 54 | 1 | no | — |
| 334 | C2×D4 | — | 54 | 2 | no | — |
| 335 | Q16 | — | 18 | 1 | no | — |
| 336 | Q16 | — | 54 | 1 | no | — |
| 337 | SD16 | — | 18 | 1 | no | — |
| 338 | SD16 | — | 54 | 1 | no | — |
| 339 | M16 | — | 3 | 1 | no | — |
| 340 | M16 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 341 | C22⋊C4 | — | 54 | 2 | no | — |
| 342 | C42 | — | 27 | 1 | no | — |
| 343 | C22×C3 | — | 2 | 1 | no | — |
| 344 | C22×C3 | — | 6 | 2 | no | — |
| 345 | C22×C3 | — | 12 | 2 | no | — |
| 346 | C22×C3 | — | 18 | 1 | no | — |
| 347 | C22×C3 | C2×D36 | 1 | 1 | yes | characteristic |
| 348 | C22×C3 | D3×D12 | 1 | 1 | yes | characteristic |
| 349 | C2×D3 | — | 2 | 2 | no | — |
| 350 | C2×D3 | — | 4 | 2 | no | — |
| 351 | C2×D3 | — | 6 | 1 | no | — |
| 352 | C2×D3 | — | 18 | 1 | no | — |
| 353 | C2×D3 | — | 18 | 1 | no | — |
| 354 | C2×D3 | — | 36 | 1 | no | — |
| 355 | C2×D3 | — | 72 | 2 | no | — |
| 356 | C2×D3 | — | 72 | 2 | no | — |
| 357 | C3×C4 | — | 2 | 1 | no | — |
| 358 | C3×C4 | — | 2 | 1 | no | — |
| 359 | C3×C4 | — | 18 | 1 | no | — |
| 360 | C3×C4 | — | 36 | 1 | no | — |
| 361 | C3×C4 | D4×D9 | 1 | 1 | yes | characteristic |
| 362 | C3×C4 | D4×D9 | 1 | 1 | yes | characteristic |
| 363 | C3×C4 | #3802 | 1 | 1 | yes | characteristic |
| 364 | C3×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 365 | Dic3 | — | 6 | 1 | no | — |
| 366 | Dic3 | — | 12 | 1 | no | — |
| 367 | Dic3 | — | 18 | 1 | no | — |
| 368 | Dic3 | — | 18 | 1 | no | — |
| 369 | Dic3 | — | 36 | 1 | no | — |
| 370 | Dic3 | — | 36 | 1 | no | — |
| 371 | Dic3 | — | 36 | 1 | no | — |
| 372 | Dic3 | — | 36 | 2 | no | — |
| 373 | C32 | #4746 | 1 | 1 | yes | characteristic |
| 374 | C9 | — | 2 | 1 | no | — |
| 375 | C9 | #5202 | 1 | 1 | yes | characteristic, complemented |
| 376 | C23 | — | 3 | 2 | no | — |
| 377 | C23 | — | 54 | 2 | no | — |
| 378 | Q8 | — | 9 | 1 | no | — |
| 379 | Q8 | — | 18 | 1 | no | — |
| 380 | Q8 | — | 18 | 1 | no | — |
| 381 | Q8 | — | 27 | 1 | no | — |
| 382 | D4 | — | 6 | 1 | no | — |
| 383 | D4 | — | 6 | 1 | no | — |
| 384 | D4 | — | 9 | 1 | no | — |
| 385 | D4 | — | 18 | 1 | no | — |
| 386 | D4 | — | 27 | 1 | no | — |
| 387 | D4 | — | 54 | 2 | no | — |
| 388 | D4 | — | 54 | 2 | no | — |
| 389 | D4 | — | 54 | 1 | no | — |
| 390 | C2×C4 | — | 18 | 1 | no | — |
| 391 | C2×C4 | — | 18 | 1 | no | — |
| 392 | C2×C4 | — | 54 | 2 | no | — |
| 393 | C2×C4 | — | 54 | 1 | no | — |
| 394 | C2×C4 | — | 54 | 1 | no | — |
| 395 | C2×C4 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 396 | C8 | — | 2 | 1 | no | — |
| 397 | C8 | — | 6 | 1 | no | — |
| 398 | C2×C3 | — | 2 | 1 | no | — |
| 399 | C2×C3 | — | 2 | 1 | no | — |
| 400 | C2×C3 | — | 2 | 1 | no | — |
| 401 | C2×C3 | — | 4 | 1 | no | — |
| 402 | C2×C3 | — | 12 | 2 | no | — |
| 403 | C2×C3 | — | 36 | 1 | no | — |
| 404 | C2×C3 | #63444 | 1 | 1 | yes | characteristic |
| 405 | C2×C3 | #63922 | 1 | 1 | yes | characteristic |
| 406 | D3 | — | 4 | 2 | no | — |
| 407 | D3 | — | 12 | 1 | no | — |
| 408 | D3 | — | 36 | 1 | no | — |
| 409 | D3 | — | 36 | 1 | no | — |
| 410 | D3 | — | 72 | 1 | no | — |
| 411 | C22 | — | 6 | 2 | no | — |
| 412 | C22 | — | 12 | 2 | no | — |
| 413 | C22 | — | 18 | 1 | no | — |
| 414 | C22 | — | 54 | 1 | no | — |
| 415 | C22 | — | 216 | 2 | no | — |
| 416 | C22 | D3×D36 | 1 | 1 | yes | characteristic |
| 417 | C4 | — | 18 | 1 | no | — |
| 418 | C4 | — | 36 | 1 | no | — |
| 419 | C4 | — | 54 | 1 | no | — |
| 420 | C4 | — | 108 | 1 | no | — |
| 421 | C4 | #88646 | 1 | 1 | yes | characteristic |
| 422 | C4 | D9×#67 | 1 | 1 | yes | characteristic |
| 423 | C3 | — | 2 | 1 | no | — |
| 424 | C3 | #10588426 | 1 | 1 | yes | characteristic, complemented |
| 425 | C3 | #10591012 | 1 | 1 | yes | characteristic |
| 426 | C2 | — | 2 | 1 | no | — |
| 427 | C2 | — | 12 | 2 | no | — |
| 428 | C2 | — | 36 | 1 | no | — |
| 429 | C2 | — | 108 | 1 | no | — |
| 430 | C2 | #11721049 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#63471 | C2 | semidirect |
| 3. #11720967 | C2 | semidirect |
| 4. #11720871 | C2 | semidirect |
| 5. #11720558 | C2 | semidirect |
| 6. C9×#823 | C2 | semidirect |
| 7. #11720291 | C2 | semidirect |
| 13. C2×C3×Dic18 | C22 | semidirect |
| 19. C3×C9×M16 | C22 | semidirect |
| 20. C4×C3⋊Dic9 | C22 | semidirect |
| 21. C9×#208 | C22 | semidirect |
| 37. #63471 | D3 | semidirect |
| 92. C2×Dic18 | C2×D3 | semidirect |
| 95. C9×M16 | C2×D3 | semidirect |
| 129. #823 | D9 | semidirect |
| 210. C3×M16 | C2×D9 | semidirect |
| 219. #208 | C2×D9 | semidirect |
| 261. C3×C9 | #455 | semidirect |
| 340. M16 | D3×D9 | semidirect |
| 375. C9 | #5202 | semidirect |
| 424. C3 | #10588426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722476 | 2 |
| C3×#63471 | 2 |
| #11720967 | 2 |
| #11720871 | 2 |
| #11720558 | 2 |
| C9×#823 | 2 |
| #11720291 | 2 |
| #10591012 | 3 |
| #10588426 | 3 |