Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
990 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 135 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 | #11722661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11721837 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721728 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×C9×#99 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11720523 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10592440 | — | 3 | 1 | no | maximal |
| 7 | #10588421 | — | 3 | 3 | no | maximal |
| 8 | C23×C3⋊D9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×C3×D4×C9 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#6233 | — | 2 | 1 | no | — |
| 11 | C2×#6233 | — | 2 | 1 | no | — |
| 12 | C2×#6233 | C22 | 1 | 2 | yes | — |
| 13 | #88742 | — | 2 | 2 | no | — |
| 14 | D4×C3⋊D9 | — | 2 | 2 | no | — |
| 15 | #88736 | — | 2 | 1 | no | — |
| 16 | C2×C4⋊(C3⋊D9) | — | 2 | 2 | no | — |
| 17 | C3×C9×C22⋊C4 | C22 | 1 | 2 | yes | complemented |
| 18 | #88551 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #88536 | — | 2 | 1 | no | — |
| 20 | #88536 | — | 2 | 2 | no | — |
| 21 | #64361 | — | 3 | 1 | no | — |
| 22 | #64146 | — | 3 | 1 | no | — |
| 23 | #64091 | — | 3 | 2 | no | — |
| 24 | #63710 | — | 3 | 3 | no | — |
| 25 | C32×#99 | D3 | 1 | 1 | yes | characteristic |
| 26 | #63633 | — | 3 | 2 | no | — |
| 27 | #63499 | — | 3 | 3 | no | — |
| 28 | #63444 | — | 3 | 6 | no | — |
| 29 | C9×#99 | D3 | 1 | 3 | yes | complemented |
| 30 | #63365 | — | 3 | 6 | no | — |
| 31 | C23×C3×C9 | D4 | 1 | 1 | yes | characteristic, complemented |
| 32 | C23×C3×C9 | C23 | 1 | 1 | yes | characteristic |
| 33 | C22×C3⋊D9 | — | 2 | 2 | no | — |
| 34 | C22×C3⋊D9 | — | 2 | 1 | no | — |
| 35 | C22×C3⋊D9 | — | 2 | 1 | no | — |
| 36 | C22×C3⋊D9 | — | 4 | 2 | no | — |
| 37 | C22×C3⋊D9 | D4 | 1 | 2 | yes | complemented |
| 38 | C3×D4×C9 | — | 2 | 2 | no | — |
| 39 | C2×C3×C4×C9 | — | 2 | 2 | no | — |
| 40 | C2×C3×C4×C9 | D4 | 1 | 1 | yes | characteristic, complemented |
| 41 | #6233 | — | 2 | 2 | no | — |
| 42 | #6233 | — | 2 | 2 | no | — |
| 43 | #6233 | — | 2 | 2 | no | — |
| 44 | #6233 | — | 4 | 2 | no | — |
| 45 | C2×C3⋊Dic9 | — | 2 | 1 | no | — |
| 46 | C2×C3⋊Dic9 | — | 2 | 1 | no | — |
| 47 | C2×C3⋊Dic9 | D4 | 1 | 2 | yes | complemented |
| 48 | C4⋊(C3⋊D9) | — | 2 | 1 | no | — |
| 49 | C4⋊(C3⋊D9) | — | 4 | 4 | no | — |
| 50 | C4×C3⋊D9 | — | 2 | 2 | no | — |
| 51 | #6226 | — | 2 | 1 | no | — |
| 52 | #4741 | — | 9 | 3 | no | — |
| 53 | #4741 | — | 9 | 1 | no | — |
| 54 | C23×C3⋊D3 | — | 3 | 1 | no | — |
| 55 | C2×C32×D4 | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | C2×#638 | — | 3 | 2 | no | — |
| 57 | C2×#638 | — | 6 | 1 | no | — |
| 58 | C2×#638 | — | 6 | 1 | no | — |
| 59 | #3830 | — | 6 | 2 | no | — |
| 60 | D4×C3⋊D3 | — | 6 | 2 | no | — |
| 61 | #3828 | — | 6 | 1 | no | — |
| 62 | C2×C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 63 | C23×D9 | — | 3 | 3 | no | — |
| 64 | C32×C22⋊C4 | C2×D3 | 1 | 2 | yes | — |
| 65 | #3757 | — | 3 | 1 | no | — |
| 66 | #3752 | — | 6 | 2 | no | — |
| 67 | #3752 | — | 6 | 1 | no | — |
| 68 | C2×D4×C9 | C2×D3 | 1 | 3 | yes | — |
| 69 | C2×#611 | — | 3 | 6 | no | — |
| 70 | C2×#611 | — | 6 | 3 | no | — |
| 71 | C2×#611 | — | 6 | 3 | no | — |
| 72 | #3699 | — | 6 | 6 | no | — |
| 73 | D4×D9 | — | 6 | 6 | no | — |
| 74 | #3697 | — | 6 | 3 | no | — |
| 75 | C2×D36 | — | 6 | 6 | no | — |
| 76 | C9×C22⋊C4 | C2×D3 | 1 | 6 | yes | complemented |
| 77 | #3676 | — | 3 | 3 | no | — |
| 78 | (C2×D9)⋊C4 | — | 6 | 6 | no | — |
| 79 | (C2×D9)⋊C4 | — | 6 | 3 | no | — |
| 80 | C22×C3×C9 | — | 2 | 1 | no | — |
| 81 | C22×C3×C9 | — | 4 | 1 | no | — |
| 82 | C22×C3×C9 | — | 4 | 1 | no | — |
| 83 | C22×C3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 84 | C22×C3×C9 | C2×D4 | 1 | 2 | yes | — |
| 85 | C2×C3⋊D9 | — | 2 | 4 | no | — |
| 86 | C2×C3⋊D9 | — | 2 | 2 | no | — |
| 87 | C2×C3⋊D9 | — | 2 | 2 | no | — |
| 88 | C2×C3⋊D9 | — | 4 | 1 | no | — |
| 89 | C2×C3⋊D9 | — | 4 | 2 | no | — |
| 90 | C2×C3⋊D9 | — | 4 | 1 | no | — |
| 91 | C2×C3⋊D9 | — | 4 | 2 | no | — |
| 92 | C2×C3⋊D9 | — | 8 | 1 | no | — |
| 93 | C3×C4×C9 | — | 2 | 1 | no | — |
| 94 | C3×C4×C9 | — | 4 | 2 | no | — |
| 95 | C3⋊Dic9 | — | 2 | 2 | no | — |
| 96 | C3⋊Dic9 | — | 4 | 1 | no | — |
| 97 | #1004 | — | 9 | 3 | no | — |
| 98 | #1004 | — | 9 | 1 | no | — |
| 99 | #937 | — | 9 | 3 | no | — |
| 100 | #937 | — | 9 | 1 | no | — |
| 101 | #882 | — | 9 | 6 | no | — |
| 102 | #882 | — | 9 | 2 | no | — |
| 103 | C3×#99 | D9 | 1 | 3 | yes | complemented |
| 104 | C3×#99 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 105 | #806 | — | 9 | 6 | no | — |
| 106 | #806 | — | 9 | 2 | no | — |
| 107 | C23×C32 | D12 | 1 | 1 | yes | characteristic |
| 108 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 109 | C22×C3⋊D3 | — | 3 | 2 | no | — |
| 110 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 111 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 112 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 113 | C22×C3⋊D3 | — | 12 | 2 | no | — |
| 114 | C32×D4 | — | 2 | 2 | no | — |
| 115 | C2×C32×C4 | — | 2 | 2 | no | — |
| 116 | C2×C32×C4 | D12 | 1 | 1 | yes | characteristic |
| 117 | #638 | — | 6 | 2 | no | — |
| 118 | #638 | — | 6 | 2 | no | — |
| 119 | #638 | — | 6 | 2 | no | — |
| 120 | #638 | — | 12 | 2 | no | — |
| 121 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 122 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 123 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 124 | C4⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 125 | C4⋊(C3⋊D3) | — | 12 | 4 | no | — |
| 126 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 127 | #634 | — | 6 | 1 | no | — |
| 128 | C23×C9 | D12 | 1 | 3 | yes | complemented |
| 129 | C23×C9 | C22×D3 | 1 | 3 | yes | — |
| 130 | C22×D9 | — | 3 | 6 | no | — |
| 131 | C22×D9 | — | 6 | 3 | no | — |
| 132 | C22×D9 | — | 6 | 6 | no | — |
| 133 | C22×D9 | — | 6 | 3 | no | — |
| 134 | C22×D9 | — | 12 | 6 | no | — |
| 135 | D4×C9 | — | 2 | 6 | no | — |
| 136 | C2×C4×C9 | — | 2 | 6 | no | — |
| 137 | C2×C4×C9 | D12 | 1 | 3 | yes | complemented |
| 138 | #611 | — | 6 | 6 | no | — |
| 139 | #611 | — | 6 | 6 | no | — |
| 140 | #611 | — | 6 | 6 | no | — |
| 141 | #611 | — | 12 | 6 | no | — |
| 142 | C2×Dic9 | — | 3 | 6 | no | — |
| 143 | C2×Dic9 | — | 6 | 3 | no | — |
| 144 | C2×Dic9 | — | 6 | 3 | no | — |
| 145 | D36 | — | 6 | 3 | no | — |
| 146 | D36 | — | 12 | 12 | no | — |
| 147 | C4×D9 | — | 6 | 6 | no | — |
| 148 | Dic18 | — | 6 | 3 | no | — |
| 149 | B(4,𝔽2) | — | 27 | 1 | no | Sylow |
| 150 | C2×C3×C9 | — | 2 | 1 | no | — |
| 151 | C2×C3×C9 | — | 2 | 2 | no | — |
| 152 | C2×C3×C9 | — | 4 | 1 | no | — |
| 153 | C2×C3×C9 | #120 | 1 | 1 | yes | characteristic |
| 154 | C3⋊D9 | — | 4 | 2 | no | — |
| 155 | C3⋊D9 | — | 4 | 2 | no | — |
| 156 | C23×D3 | — | 9 | 3 | no | — |
| 157 | C23×D3 | — | 9 | 1 | no | — |
| 158 | C2×C3×D4 | C2×D9 | 1 | 3 | yes | — |
| 159 | C2×C3×D4 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 160 | C2×#67 | — | 9 | 6 | no | — |
| 161 | C2×#67 | — | 9 | 2 | no | — |
| 162 | C2×#67 | — | 18 | 3 | no | — |
| 163 | C2×#67 | — | 18 | 1 | no | — |
| 164 | C2×#67 | — | 18 | 3 | no | — |
| 165 | C2×#67 | — | 18 | 1 | no | — |
| 166 | #237 | — | 18 | 2 | no | — |
| 167 | #237 | — | 18 | 6 | no | — |
| 168 | D3×D4 | — | 18 | 2 | no | — |
| 169 | D3×D4 | — | 18 | 6 | no | — |
| 170 | #235 | — | 18 | 3 | no | — |
| 171 | #235 | — | 18 | 1 | no | — |
| 172 | C2×D12 | — | 18 | 2 | no | — |
| 173 | C2×D12 | — | 18 | 6 | no | — |
| 174 | C3×C22⋊C4 | C2×D9 | 1 | 6 | yes | complemented |
| 175 | C3×C22⋊C4 | C2×C3⋊D3 | 1 | 2 | yes | — |
| 176 | #217 | — | 9 | 3 | no | — |
| 177 | #217 | — | 9 | 1 | no | — |
| 178 | (C2×D3)⋊C4 | — | 18 | 2 | no | — |
| 179 | (C2×D3)⋊C4 | — | 18 | 6 | no | — |
| 180 | (C2×D3)⋊C4 | — | 18 | 3 | no | — |
| 181 | (C2×D3)⋊C4 | — | 18 | 1 | no | — |
| 182 | C22×C32 | — | 2 | 1 | no | — |
| 183 | C22×C32 | — | 4 | 1 | no | — |
| 184 | C22×C32 | — | 4 | 1 | no | — |
| 185 | C22×C32 | C2×D12 | 1 | 1 | yes | characteristic |
| 186 | C22×C32 | D3×D4 | 1 | 2 | yes | — |
| 187 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 188 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 189 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 190 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 191 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 192 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 193 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 194 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 195 | C32×C4 | — | 2 | 1 | no | — |
| 196 | C32×C4 | — | 4 | 2 | no | — |
| 197 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 198 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 199 | C22×C9 | — | 2 | 3 | no | — |
| 200 | C22×C9 | — | 4 | 3 | no | — |
| 201 | C22×C9 | — | 4 | 3 | no | — |
| 202 | C22×C9 | C2×D12 | 1 | 3 | yes | — |
| 203 | C22×C9 | D3×D4 | 1 | 6 | yes | — |
| 204 | C2×D9 | — | 6 | 12 | no | — |
| 205 | C2×D9 | — | 6 | 6 | no | — |
| 206 | C2×D9 | — | 6 | 6 | no | — |
| 207 | C2×D9 | — | 12 | 3 | no | — |
| 208 | C2×D9 | — | 12 | 6 | no | — |
| 209 | C2×D9 | — | 12 | 3 | no | — |
| 210 | C2×D9 | — | 12 | 6 | no | — |
| 211 | C2×D9 | — | 24 | 3 | no | — |
| 212 | C4×C9 | — | 2 | 3 | no | — |
| 213 | C4×C9 | — | 4 | 6 | no | — |
| 214 | Dic9 | — | 6 | 6 | no | — |
| 215 | Dic9 | — | 12 | 3 | no | — |
| 216 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 217 | #120 | — | 27 | 1 | no | — |
| 218 | #120 | — | 27 | 2 | no | — |
| 219 | #99 | — | 27 | 2 | no | — |
| 220 | #99 | C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 221 | C3×C9 | B(4,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 222 | C23×C3 | D36 | 1 | 3 | yes | complemented |
| 223 | C23×C3 | C22×D9 | 1 | 3 | yes | — |
| 224 | C23×C3 | C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 225 | C23×C3 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 226 | C22×D3 | — | 9 | 6 | no | — |
| 227 | C22×D3 | — | 9 | 2 | no | — |
| 228 | C22×D3 | — | 18 | 3 | no | — |
| 229 | C22×D3 | — | 18 | 6 | no | — |
| 230 | C22×D3 | — | 18 | 1 | no | — |
| 231 | C22×D3 | — | 18 | 2 | no | — |
| 232 | C22×D3 | — | 18 | 1 | no | — |
| 233 | C22×D3 | — | 18 | 3 | no | — |
| 234 | C22×D3 | — | 36 | 2 | no | — |
| 235 | C22×D3 | — | 36 | 6 | no | — |
| 236 | C3×D4 | — | 2 | 6 | no | — |
| 237 | C3×D4 | — | 2 | 2 | no | — |
| 238 | C2×C3×C4 | — | 2 | 6 | no | — |
| 239 | C2×C3×C4 | — | 2 | 2 | no | — |
| 240 | C2×C3×C4 | D36 | 1 | 3 | yes | complemented |
| 241 | C2×C3×C4 | C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 242 | #67 | — | 18 | 2 | no | — |
| 243 | #67 | — | 18 | 6 | no | — |
| 244 | #67 | — | 18 | 6 | no | — |
| 245 | #67 | — | 18 | 6 | no | — |
| 246 | #67 | — | 18 | 2 | no | — |
| 247 | #67 | — | 18 | 2 | no | — |
| 248 | #67 | — | 36 | 2 | no | — |
| 249 | #67 | — | 36 | 6 | no | — |
| 250 | C2×Dic3 | — | 9 | 6 | no | — |
| 251 | C2×Dic3 | — | 9 | 2 | no | — |
| 252 | C2×Dic3 | — | 18 | 1 | no | — |
| 253 | C2×Dic3 | — | 18 | 3 | no | — |
| 254 | C2×Dic3 | — | 18 | 3 | no | — |
| 255 | C2×Dic3 | — | 18 | 1 | no | — |
| 256 | D12 | — | 18 | 1 | no | — |
| 257 | D12 | — | 18 | 3 | no | — |
| 258 | D12 | — | 36 | 4 | no | — |
| 259 | D12 | — | 36 | 12 | no | — |
| 260 | C4×D3 | — | 18 | 2 | no | — |
| 261 | C4×D3 | — | 18 | 6 | no | — |
| 262 | Dic6 | — | 18 | 1 | no | — |
| 263 | Dic6 | — | 18 | 3 | no | — |
| 264 | C2×C32 | — | 2 | 1 | no | — |
| 265 | C2×C32 | — | 2 | 2 | no | — |
| 266 | C2×C32 | — | 4 | 1 | no | — |
| 267 | C2×C32 | #882 | 1 | 1 | yes | characteristic |
| 268 | C3⋊D3 | — | 12 | 2 | no | — |
| 269 | C3⋊D3 | — | 12 | 2 | no | — |
| 270 | C2×C9 | — | 2 | 3 | no | — |
| 271 | C2×C9 | — | 2 | 6 | no | — |
| 272 | C2×C9 | — | 4 | 3 | no | — |
| 273 | C2×C9 | #882 | 1 | 3 | yes | — |
| 274 | D9 | — | 12 | 6 | no | — |
| 275 | D9 | — | 12 | 6 | no | — |
| 276 | C24 | — | 27 | 1 | no | — |
| 277 | #41 | — | 54 | 2 | no | — |
| 278 | #41 | — | 54 | 1 | no | — |
| 279 | C2×D4 | — | 27 | 2 | no | — |
| 280 | C2×D4 | — | 54 | 2 | no | — |
| 281 | C2×D4 | — | 54 | 2 | no | — |
| 282 | C2×D4 | — | 54 | 1 | no | — |
| 283 | C2×D4 | — | 54 | 1 | no | — |
| 284 | C2×D4 | C2×C3⋊D9 | 1 | 1 | yes | characteristic |
| 285 | C22⋊C4 | — | 27 | 1 | no | — |
| 286 | C22⋊C4 | — | 54 | 2 | no | — |
| 287 | C22⋊C4 | — | 54 | 1 | no | — |
| 288 | C22⋊C4 | C2×C3⋊D9 | 1 | 2 | yes | complemented |
| 289 | C22×C3 | — | 2 | 1 | no | — |
| 290 | C22×C3 | — | 2 | 3 | no | — |
| 291 | C22×C3 | — | 4 | 3 | no | — |
| 292 | C22×C3 | — | 4 | 1 | no | — |
| 293 | C22×C3 | — | 4 | 3 | no | — |
| 294 | C22×C3 | — | 4 | 1 | no | — |
| 295 | C22×C3 | C2×D36 | 1 | 3 | yes | — |
| 296 | C22×C3 | D4×D9 | 1 | 6 | yes | — |
| 297 | C22×C3 | C2×C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 298 | C22×C3 | D4×C3⋊D3 | 1 | 2 | yes | — |
| 299 | C2×D3 | — | 18 | 4 | no | — |
| 300 | C2×D3 | — | 18 | 12 | no | — |
| 301 | C2×D3 | — | 18 | 2 | no | — |
| 302 | C2×D3 | — | 18 | 6 | no | — |
| 303 | C2×D3 | — | 18 | 2 | no | — |
| 304 | C2×D3 | — | 18 | 6 | no | — |
| 305 | C2×D3 | — | 36 | 1 | no | — |
| 306 | C2×D3 | — | 36 | 2 | no | — |
| 307 | C2×D3 | — | 36 | 3 | no | — |
| 308 | C2×D3 | — | 36 | 6 | no | — |
| 309 | C2×D3 | — | 36 | 1 | no | — |
| 310 | C2×D3 | — | 36 | 3 | no | — |
| 311 | C2×D3 | — | 36 | 2 | no | — |
| 312 | C2×D3 | — | 36 | 6 | no | — |
| 313 | C2×D3 | — | 72 | 1 | no | — |
| 314 | C2×D3 | — | 72 | 3 | no | — |
| 315 | C3×C4 | — | 2 | 1 | no | — |
| 316 | C3×C4 | — | 2 | 3 | no | — |
| 317 | C3×C4 | — | 4 | 2 | no | — |
| 318 | C3×C4 | — | 4 | 6 | no | — |
| 319 | Dic3 | — | 18 | 2 | no | — |
| 320 | Dic3 | — | 18 | 6 | no | — |
| 321 | Dic3 | — | 36 | 1 | no | — |
| 322 | Dic3 | — | 36 | 3 | no | — |
| 323 | C32 | #4741 | 1 | 1 | yes | characteristic |
| 324 | C9 | #4741 | 1 | 3 | yes | complemented |
| 325 | C23 | — | 27 | 2 | no | — |
| 326 | C23 | — | 54 | 1 | no | — |
| 327 | C23 | — | 54 | 1 | no | — |
| 328 | C23 | — | 54 | 2 | no | — |
| 329 | C23 | — | 108 | 2 | no | — |
| 330 | C23 | C4⋊(C3⋊D9) | 1 | 1 | yes | characteristic, complemented |
| 331 | C23 | C22×C3⋊D9 | 1 | 1 | yes | characteristic |
| 332 | Q8 | — | 54 | 1 | no | — |
| 333 | D4 | — | 2 | 2 | no | — |
| 334 | D4 | — | 54 | 1 | no | — |
| 335 | D4 | — | 54 | 2 | no | — |
| 336 | D4 | — | 54 | 2 | no | — |
| 337 | D4 | — | 54 | 2 | no | — |
| 338 | D4 | — | 108 | 4 | no | — |
| 339 | D4 | — | 108 | 2 | no | — |
| 340 | C2×C4 | — | 2 | 2 | no | — |
| 341 | C2×C4 | — | 27 | 2 | no | — |
| 342 | C2×C4 | — | 54 | 2 | no | — |
| 343 | C2×C4 | — | 54 | 1 | no | — |
| 344 | C2×C4 | — | 54 | 1 | no | — |
| 345 | C2×C4 | C4⋊(C3⋊D9) | 1 | 1 | yes | characteristic, complemented |
| 346 | C2×C3 | — | 2 | 3 | no | — |
| 347 | C2×C3 | — | 2 | 6 | no | — |
| 348 | C2×C3 | — | 2 | 1 | no | — |
| 349 | C2×C3 | — | 2 | 2 | no | — |
| 350 | C2×C3 | — | 4 | 3 | no | — |
| 351 | C2×C3 | — | 4 | 1 | no | — |
| 352 | C2×C3 | #63444 | 1 | 3 | yes | — |
| 353 | C2×C3 | #64091 | 1 | 1 | yes | characteristic |
| 354 | D3 | — | 36 | 6 | no | — |
| 355 | D3 | — | 36 | 6 | no | — |
| 356 | D3 | — | 36 | 2 | no | — |
| 357 | D3 | — | 36 | 2 | no | — |
| 358 | C22 | — | 2 | 1 | no | — |
| 359 | C22 | — | 4 | 1 | no | — |
| 360 | C22 | — | 4 | 1 | no | — |
| 361 | C22 | — | 54 | 4 | no | — |
| 362 | C22 | — | 54 | 2 | no | — |
| 363 | C22 | — | 54 | 2 | no | — |
| 364 | C22 | — | 108 | 2 | no | — |
| 365 | C22 | — | 108 | 2 | no | — |
| 366 | C22 | — | 108 | 1 | no | — |
| 367 | C22 | — | 108 | 1 | no | — |
| 368 | C22 | — | 216 | 1 | no | — |
| 369 | C22 | C2×C4⋊(C3⋊D9) | 1 | 1 | yes | characteristic |
| 370 | C22 | D4×C3⋊D9 | 1 | 2 | yes | — |
| 371 | C4 | — | 2 | 1 | no | — |
| 372 | C4 | — | 4 | 2 | no | — |
| 373 | C4 | — | 54 | 2 | no | — |
| 374 | C4 | — | 108 | 1 | no | — |
| 375 | C3 | #10588421 | 1 | 3 | yes | complemented |
| 376 | C3 | #10592440 | 1 | 1 | yes | characteristic |
| 377 | C2 | — | 2 | 2 | no | — |
| 378 | C2 | — | 2 | 1 | no | — |
| 379 | C2 | — | 4 | 1 | no | — |
| 380 | C2 | — | 108 | 2 | no | — |
| 381 | C2 | — | 108 | 2 | no | — |
| 382 | C2 | #11721728 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722661 | C2 | semidirect |
| 2. #11721837 | C2 | semidirect |
| 3. #11721728 | C2 | semidirect |
| 4. C3×C9×#99 | C2 | semidirect |
| 5. #11720523 | C2 | semidirect |
| 8. C23×C3⋊D9 | C22 | semidirect |
| 17. C3×C9×C22⋊C4 | C22 | semidirect |
| 18. #88551 | C22 | semidirect |
| 29. C9×#99 | D3 | semidirect |
| 31. C23×C3×C9 | D4 | semidirect |
| 37. C22×C3⋊D9 | D4 | semidirect |
| 40. C2×C3×C4×C9 | D4 | semidirect |
| 47. C2×C3⋊Dic9 | D4 | semidirect |
| 76. C9×C22⋊C4 | C2×D3 | semidirect |
| 103. C3×#99 | D9 | semidirect |
| 128. C23×C9 | D12 | semidirect |
| 137. C2×C4×C9 | D12 | semidirect |
| 174. C3×C22⋊C4 | C2×D9 | semidirect |
| 220. #99 | C3⋊D9 | semidirect |
| 221. C3×C9 | B(4,𝔽2) | semidirect |
| 222. C23×C3 | D36 | semidirect |
| 240. C2×C3×C4 | D36 | semidirect |
| 288. C22⋊C4 | C2×C3⋊D9 | semidirect |
| 324. C9 | #4741 | semidirect |
| 330. C23 | C4⋊(C3⋊D9) | semidirect |
| 345. C2×C4 | C4⋊(C3⋊D9) | semidirect |
| 375. C3 | #10588421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722661 | 2 |
| #11721837 | 2 |
| #11721728 | 2 |
| C3×C9×#99 | 2 |
| #11720523 | 2 |
| #10592440 | 3 |
| #10588421 | 3 |