Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
954 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 37 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 | D3×C22⋊(C22⋊C9) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3⋊#64188 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#64188 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#64188 | — | 3 | 1 | no | maximal |
| 5 | D3×#953 | — | 3 | 1 | no | maximal |
| 6 | C3×C22⋊(C22⋊C9) | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | D3×(C22⋊C9)⋊C2 | — | 4 | 3 | no | maximal |
| 8 | C24×C3×D3 | D3 | 1 | 1 | yes | characteristic |
| 9 | C2×D3×#67 | — | 3 | 3 | no | — |
| 10 | C2×C22⋊(C22⋊C9) | — | 3 | 1 | no | — |
| 11 | #64188 | — | 3 | 1 | no | — |
| 12 | #64188 | — | 6 | 1 | no | — |
| 13 | #64188 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 14 | #64162 | — | 3 | 1 | no | — |
| 15 | C3×#953 | — | 3 | 1 | no | — |
| 16 | #63977 | — | 3 | 3 | no | — |
| 17 | #63976 | — | 3 | 3 | no | — |
| 18 | D3×#217 | — | 3 | 3 | no | — |
| 19 | D3×C22⋊C9 | — | 4 | 3 | no | — |
| 20 | D3×C22⋊C9 | — | 8 | 1 | no | — |
| 21 | C3⋊((C22⋊C9)⋊C2) | — | 4 | 3 | no | — |
| 22 | C3×(C22⋊C9)⋊C2 | — | 4 | 3 | no | — |
| 23 | C2×#953 | — | 9 | 1 | no | — |
| 24 | D3×#120 | — | 9 | 1 | no | — |
| 25 | C24×C32 | C2×D3 | 1 | 1 | yes | characteristic |
| 26 | C23×C3×D3 | — | 3 | 3 | no | — |
| 27 | C23×C3×D3 | — | 3 | 3 | no | — |
| 28 | C23×C3×D3 | — | 6 | 1 | no | — |
| 29 | C23×C3×D3 | — | 6 | 1 | no | — |
| 30 | C22×D32 | — | 3 | 1 | no | — |
| 31 | C2×#638 | — | 3 | 3 | no | — |
| 32 | C2×C3×#67 | — | 3 | 3 | no | — |
| 33 | D3×#67 | — | 6 | 3 | no | — |
| 34 | D3×#67 | — | 6 | 3 | no | — |
| 35 | D3×#67 | — | 6 | 3 | no | — |
| 36 | D3×#67 | — | 6 | 3 | no | — |
| 37 | C2×#626 | — | 3 | 3 | no | — |
| 38 | C2×#625 | — | 3 | 3 | no | — |
| 39 | C2×D3×Dic3 | — | 3 | 3 | no | — |
| 40 | C22⋊(C22⋊C9) | — | 2 | 1 | no | — |
| 41 | C22⋊(C22⋊C9) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 42 | C2×(C22⋊C9)⋊C2 | — | 12 | 3 | no | — |
| 43 | #3757 | — | 3 | 3 | no | — |
| 44 | C3×#217 | — | 3 | 3 | no | — |
| 45 | (C2×D3)⋊Dic3 | — | 3 | 6 | no | — |
| 46 | C3×C22⋊C9 | — | 4 | 3 | no | — |
| 47 | C3×C22⋊C9 | — | 8 | 1 | no | — |
| 48 | D3×D9 | — | 16 | 1 | no | — |
| 49 | C25×C3 | — | 3 | 1 | no | — |
| 50 | C24×D3 | D9 | 1 | 1 | yes | characteristic, complemented |
| 51 | C22×#67 | — | 9 | 3 | no | — |
| 52 | C2×D3×D4 | — | 9 | 3 | no | — |
| 53 | C3×#120 | — | 9 | 1 | no | — |
| 54 | #953 | — | 3 | 1 | no | — |
| 55 | #953 | — | 9 | 3 | no | — |
| 56 | #953 | — | 9 | 3 | no | — |
| 57 | #953 | — | 9 | 1 | no | — |
| 58 | #953 | — | 9 | 1 | no | — |
| 59 | #953 | — | 18 | 1 | no | — |
| 60 | C2×#217 | — | 9 | 3 | no | — |
| 61 | #937 | — | 9 | 3 | no | — |
| 62 | #882 | — | 9 | 3 | no | — |
| 63 | D3×C22⋊C4 | — | 9 | 3 | no | — |
| 64 | C23×C32 | — | 3 | 3 | no | — |
| 65 | C23×C32 | — | 6 | 1 | no | — |
| 66 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 67 | C22×C3×D3 | — | 2 | 1 | no | — |
| 68 | C22×C3×D3 | — | 3 | 1 | no | — |
| 69 | C22×C3×D3 | — | 3 | 3 | no | — |
| 70 | C22×C3×D3 | — | 3 | 3 | no | — |
| 71 | C22×C3×D3 | — | 3 | 3 | no | — |
| 72 | C22×C3×D3 | — | 3 | 3 | no | — |
| 73 | C22×C3×D3 | — | 3 | 1 | no | — |
| 74 | C22×C3×D3 | — | 6 | 6 | no | — |
| 75 | C22×C3×D3 | — | 6 | 3 | no | — |
| 76 | C22×C3×D3 | — | 6 | 3 | no | — |
| 77 | C22×C3×D3 | — | 6 | 1 | no | — |
| 78 | C22×C3×D3 | — | 6 | 3 | no | — |
| 79 | C22×C3×D3 | S4 | 1 | 3 | yes | — |
| 80 | C2×D32 | — | 6 | 3 | no | — |
| 81 | C2×D32 | — | 6 | 3 | no | — |
| 82 | #638 | — | 6 | 3 | no | — |
| 83 | #638 | — | 6 | 3 | no | — |
| 84 | C2×C3⋊Dic3 | — | 3 | 3 | no | — |
| 85 | C3×#67 | — | 6 | 3 | no | — |
| 86 | C3×#67 | — | 6 | 3 | no | — |
| 87 | C2×C3×Dic3 | — | 3 | 3 | no | — |
| 88 | #626 | — | 6 | 3 | no | — |
| 89 | #626 | — | 6 | 3 | no | — |
| 90 | #625 | — | 6 | 3 | no | — |
| 91 | #625 | — | 6 | 3 | no | — |
| 92 | D3×Dic3 | — | 6 | 3 | no | — |
| 93 | D3×Dic3 | — | 6 | 3 | no | — |
| 94 | C2×C22⋊C9 | — | 12 | 3 | no | — |
| 95 | C2×C22⋊C9 | — | 24 | 1 | no | — |
| 96 | (C22⋊C9)⋊C2 | — | 4 | 3 | no | — |
| 97 | (C22⋊C9)⋊C2 | — | 12 | 3 | no | — |
| 98 | (C22⋊C9)⋊C2 | — | 24 | 3 | no | — |
| 99 | C2×#120 | — | 27 | 1 | no | Sylow |
| 100 | C3⋊D9 | — | 16 | 1 | no | — |
| 101 | D3×C9 | — | 16 | 1 | no | — |
| 102 | C3×D9 | — | 16 | 1 | no | — |
| 103 | C24×C3 | — | 2 | 1 | no | — |
| 104 | C24×C3 | — | 9 | 3 | no | — |
| 105 | C24×C3 | — | 9 | 3 | no | — |
| 106 | C24×C3 | — | 18 | 1 | no | — |
| 107 | C24×C3 | — | 18 | 1 | no | — |
| 108 | C24×C3 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 109 | C24×C3 | D32 | 1 | 1 | yes | characteristic |
| 110 | C23×D3 | — | 3 | 3 | no | — |
| 111 | C23×D3 | — | 3 | 3 | no | — |
| 112 | C23×D3 | — | 6 | 1 | no | — |
| 113 | C23×D3 | — | 6 | 1 | no | — |
| 114 | C23×D3 | — | 9 | 1 | no | — |
| 115 | C23×D3 | — | 9 | 1 | no | — |
| 116 | C2×C3×D4 | — | 9 | 3 | no | — |
| 117 | C2×#67 | — | 3 | 3 | no | — |
| 118 | C2×#67 | — | 9 | 3 | no | — |
| 119 | C2×#67 | — | 9 | 3 | no | — |
| 120 | C2×#67 | — | 9 | 3 | no | — |
| 121 | C2×#67 | — | 9 | 3 | no | — |
| 122 | C2×#67 | — | 9 | 3 | no | — |
| 123 | C2×#67 | — | 18 | 3 | no | — |
| 124 | C2×#67 | — | 18 | 3 | no | — |
| 125 | C2×#67 | — | 18 | 3 | no | — |
| 126 | C2×#67 | — | 18 | 3 | no | — |
| 127 | C2×#67 | — | 18 | 3 | no | — |
| 128 | C22×Dic3 | — | 9 | 3 | no | — |
| 129 | D3×D4 | — | 18 | 3 | no | — |
| 130 | D3×D4 | — | 18 | 3 | no | — |
| 131 | D3×D4 | — | 18 | 3 | no | — |
| 132 | D3×D4 | — | 18 | 3 | no | — |
| 133 | C2×D12 | — | 9 | 3 | no | — |
| 134 | C2×C4×D3 | — | 9 | 3 | no | — |
| 135 | C3×C22⋊C4 | — | 9 | 3 | no | — |
| 136 | #217 | — | 3 | 3 | no | — |
| 137 | #217 | — | 9 | 6 | no | — |
| 138 | #217 | — | 9 | 3 | no | — |
| 139 | #217 | — | 9 | 3 | no | — |
| 140 | #217 | — | 18 | 3 | no | — |
| 141 | (C2×D3)⋊C4 | — | 9 | 6 | no | — |
| 142 | C22×C32 | — | 2 | 1 | no | — |
| 143 | C22×C32 | — | 3 | 1 | no | — |
| 144 | C22×C32 | — | 3 | 3 | no | — |
| 145 | C22×C32 | — | 6 | 3 | no | — |
| 146 | C22×C32 | C2×S4 | 1 | 3 | yes | — |
| 147 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 148 | C2×C3×D3 | — | 3 | 3 | no | — |
| 149 | C2×C3×D3 | — | 3 | 3 | no | — |
| 150 | C2×C3×D3 | — | 3 | 3 | no | — |
| 151 | C2×C3×D3 | — | 3 | 3 | no | — |
| 152 | C2×C3×D3 | — | 6 | 3 | no | — |
| 153 | C2×C3×D3 | — | 6 | 6 | no | — |
| 154 | C2×C3×D3 | — | 6 | 3 | no | — |
| 155 | C2×C3×D3 | — | 6 | 1 | no | — |
| 156 | C2×C3×D3 | — | 6 | 1 | no | — |
| 157 | C2×C3×D3 | — | 6 | 3 | no | — |
| 158 | D32 | — | 12 | 3 | no | — |
| 159 | D32 | — | 12 | 1 | no | — |
| 160 | C3⋊Dic3 | — | 6 | 3 | no | — |
| 161 | C3×Dic3 | — | 6 | 3 | no | — |
| 162 | C2×D9 | — | 48 | 1 | no | — |
| 163 | C22⋊C9 | — | 4 | 3 | no | — |
| 164 | C22⋊C9 | — | 8 | 1 | no | — |
| 165 | C22⋊C9 | — | 8 | 3 | no | — |
| 166 | C22⋊C9 | — | 16 | 1 | no | — |
| 167 | C25 | — | 3 | 1 | no | — |
| 168 | C22×D4 | — | 27 | 3 | no | — |
| 169 | #120 | — | 9 | 1 | no | — |
| 170 | #120 | — | 27 | 3 | no | — |
| 171 | #120 | — | 27 | 3 | no | — |
| 172 | #120 | — | 27 | 1 | no | — |
| 173 | C2×C22⋊C4 | — | 27 | 3 | no | — |
| 174 | C3×C9 | — | 16 | 1 | no | Sylow |
| 175 | C23×C3 | — | 3 | 3 | no | — |
| 176 | C23×C3 | — | 3 | 3 | no | — |
| 177 | C23×C3 | — | 3 | 3 | no | — |
| 178 | C23×C3 | — | 6 | 3 | no | — |
| 179 | C23×C3 | — | 6 | 1 | no | — |
| 180 | C23×C3 | — | 6 | 1 | no | — |
| 181 | C23×C3 | — | 6 | 1 | no | — |
| 182 | C23×C3 | — | 9 | 1 | no | — |
| 183 | C23×C3 | — | 9 | 3 | no | — |
| 184 | C23×C3 | — | 9 | 3 | no | — |
| 185 | C23×C3 | — | 9 | 3 | no | — |
| 186 | C23×C3 | — | 9 | 1 | no | — |
| 187 | C23×C3 | — | 9 | 3 | no | — |
| 188 | C23×C3 | — | 12 | 1 | no | — |
| 189 | C23×C3 | — | 18 | 1 | no | — |
| 190 | C23×C3 | — | 18 | 3 | no | — |
| 191 | C23×C3 | — | 18 | 3 | no | — |
| 192 | C23×C3 | — | 18 | 6 | no | — |
| 193 | C23×C3 | — | 18 | 3 | no | — |
| 194 | C22×D3 | — | 2 | 1 | no | — |
| 195 | C22×D3 | — | 3 | 1 | no | — |
| 196 | C22×D3 | — | 3 | 3 | no | — |
| 197 | C22×D3 | — | 3 | 3 | no | — |
| 198 | C22×D3 | — | 3 | 3 | no | — |
| 199 | C22×D3 | — | 3 | 3 | no | — |
| 200 | C22×D3 | — | 3 | 1 | no | — |
| 201 | C22×D3 | — | 6 | 6 | no | — |
| 202 | C22×D3 | — | 6 | 3 | no | — |
| 203 | C22×D3 | — | 6 | 3 | no | — |
| 204 | C22×D3 | — | 6 | 1 | no | — |
| 205 | C22×D3 | — | 6 | 3 | no | — |
| 206 | C22×D3 | — | 9 | 1 | no | — |
| 207 | C22×D3 | — | 9 | 1 | no | — |
| 208 | C22×D3 | — | 18 | 1 | no | — |
| 209 | C22×D3 | — | 18 | 3 | no | — |
| 210 | C22×D3 | — | 18 | 3 | no | — |
| 211 | C22×D3 | — | 18 | 3 | no | — |
| 212 | C22×D3 | — | 18 | 3 | no | — |
| 213 | C22×D3 | (C22⋊C9)⋊C2 | 1 | 3 | yes | complemented |
| 214 | C3×D4 | — | 18 | 3 | no | — |
| 215 | C3×D4 | — | 18 | 3 | no | — |
| 216 | C2×C3×C4 | — | 9 | 3 | no | — |
| 217 | #67 | — | 6 | 3 | no | — |
| 218 | #67 | — | 6 | 3 | no | — |
| 219 | #67 | — | 18 | 3 | no | — |
| 220 | #67 | — | 18 | 3 | no | — |
| 221 | #67 | — | 18 | 3 | no | — |
| 222 | #67 | — | 18 | 3 | no | — |
| 223 | #67 | — | 18 | 3 | no | — |
| 224 | #67 | — | 18 | 3 | no | — |
| 225 | #67 | — | 18 | 3 | no | — |
| 226 | #67 | — | 18 | 3 | no | — |
| 227 | #67 | — | 18 | 3 | no | — |
| 228 | #67 | — | 18 | 3 | no | — |
| 229 | #67 | — | 36 | 3 | no | — |
| 230 | #67 | — | 36 | 3 | no | — |
| 231 | C2×Dic3 | — | 3 | 3 | no | — |
| 232 | C2×Dic3 | — | 9 | 3 | no | — |
| 233 | C2×Dic3 | — | 9 | 3 | no | — |
| 234 | C2×Dic3 | — | 18 | 3 | no | — |
| 235 | C2×Dic3 | — | 18 | 3 | no | — |
| 236 | C2×Dic3 | — | 18 | 3 | no | — |
| 237 | D12 | — | 18 | 3 | no | — |
| 238 | D12 | — | 18 | 3 | no | — |
| 239 | C4×D3 | — | 18 | 3 | no | — |
| 240 | C4×D3 | — | 18 | 3 | no | — |
| 241 | C2×C32 | — | 3 | 3 | no | — |
| 242 | C2×C32 | — | 6 | 1 | no | — |
| 243 | C3⋊D3 | — | 12 | 1 | no | — |
| 244 | C3×D3 | — | 3 | 3 | no | — |
| 245 | C3×D3 | — | 6 | 1 | no | — |
| 246 | C3×D3 | — | 12 | 1 | no | — |
| 247 | C3×D3 | #1020 | 1 | 1 | yes | characteristic |
| 248 | C2×C9 | — | 48 | 1 | no | — |
| 249 | D9 | — | 16 | 1 | no | — |
| 250 | D9 | — | 48 | 1 | no | — |
| 251 | D9 | — | 96 | 1 | no | — |
| 252 | C24 | — | 9 | 3 | no | — |
| 253 | C24 | — | 9 | 3 | no | — |
| 254 | C24 | — | 18 | 1 | no | — |
| 255 | C24 | — | 18 | 1 | no | — |
| 256 | C24 | — | 27 | 1 | no | — |
| 257 | C24 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 258 | C2×D4 | — | 9 | 3 | no | — |
| 259 | C2×D4 | — | 27 | 3 | no | — |
| 260 | C2×D4 | — | 27 | 3 | no | — |
| 261 | C2×D4 | — | 27 | 3 | no | — |
| 262 | C2×D4 | — | 54 | 3 | no | — |
| 263 | C2×D4 | — | 54 | 3 | no | — |
| 264 | C2×D4 | — | 54 | 3 | no | — |
| 265 | C2×D4 | — | 54 | 3 | no | — |
| 266 | C22×C4 | — | 27 | 3 | no | — |
| 267 | C22⋊C4 | — | 9 | 3 | no | — |
| 268 | C22⋊C4 | — | 27 | 6 | no | — |
| 269 | C22⋊C4 | — | 27 | 3 | no | — |
| 270 | C22×C3 | — | 2 | 1 | no | — |
| 271 | C22×C3 | — | 2 | 1 | no | — |
| 272 | C22×C3 | — | 2 | 3 | no | — |
| 273 | C22×C3 | — | 3 | 1 | no | — |
| 274 | C22×C3 | — | 3 | 1 | no | — |
| 275 | C22×C3 | — | 3 | 3 | no | — |
| 276 | C22×C3 | — | 3 | 3 | no | — |
| 277 | C22×C3 | — | 4 | 1 | no | — |
| 278 | C22×C3 | — | 6 | 1 | no | — |
| 279 | C22×C3 | — | 6 | 3 | no | — |
| 280 | C22×C3 | — | 6 | 3 | no | — |
| 281 | C22×C3 | — | 6 | 3 | no | — |
| 282 | C22×C3 | — | 9 | 3 | no | — |
| 283 | C22×C3 | — | 9 | 3 | no | — |
| 284 | C22×C3 | — | 9 | 3 | no | — |
| 285 | C22×C3 | — | 9 | 3 | no | — |
| 286 | C22×C3 | — | 12 | 3 | no | — |
| 287 | C22×C3 | — | 18 | 1 | no | — |
| 288 | C22×C3 | — | 18 | 6 | no | — |
| 289 | C22×C3 | — | 18 | 3 | no | — |
| 290 | C22×C3 | — | 18 | 3 | no | — |
| 291 | C22×C3 | — | 18 | 3 | no | — |
| 292 | C22×C3 | — | 18 | 1 | no | — |
| 293 | C22×C3 | C2×(C22⋊C9)⋊C2 | 1 | 3 | yes | complemented |
| 294 | C22×C3 | D3×S4 | 1 | 3 | yes | — |
| 295 | C2×D3 | — | 3 | 3 | no | — |
| 296 | C2×D3 | — | 3 | 3 | no | — |
| 297 | C2×D3 | — | 3 | 3 | no | — |
| 298 | C2×D3 | — | 3 | 3 | no | — |
| 299 | C2×D3 | — | 6 | 3 | no | — |
| 300 | C2×D3 | — | 6 | 6 | no | — |
| 301 | C2×D3 | — | 6 | 3 | no | — |
| 302 | C2×D3 | — | 6 | 1 | no | — |
| 303 | C2×D3 | — | 6 | 1 | no | — |
| 304 | C2×D3 | — | 6 | 3 | no | — |
| 305 | C2×D3 | — | 18 | 3 | no | — |
| 306 | C2×D3 | — | 18 | 3 | no | — |
| 307 | C2×D3 | — | 36 | 3 | no | — |
| 308 | C2×D3 | — | 36 | 3 | no | — |
| 309 | C2×D3 | — | 36 | 1 | no | — |
| 310 | C2×D3 | — | 36 | 3 | no | — |
| 311 | C2×D3 | — | 36 | 1 | no | — |
| 312 | C3×C4 | — | 18 | 3 | no | — |
| 313 | Dic3 | — | 6 | 3 | no | — |
| 314 | Dic3 | — | 18 | 3 | no | — |
| 315 | Dic3 | — | 18 | 3 | no | — |
| 316 | Dic3 | — | 36 | 3 | no | — |
| 317 | C32 | C2×#1020 | 1 | 1 | yes | characteristic |
| 318 | C9 | — | 16 | 1 | no | — |
| 319 | C9 | — | 32 | 1 | no | — |
| 320 | C23 | — | 3 | 3 | no | — |
| 321 | C23 | — | 3 | 3 | no | — |
| 322 | C23 | — | 6 | 1 | no | — |
| 323 | C23 | — | 6 | 1 | no | — |
| 324 | C23 | — | 9 | 1 | no | — |
| 325 | C23 | — | 9 | 3 | no | — |
| 326 | C23 | — | 9 | 3 | no | — |
| 327 | C23 | — | 9 | 3 | no | — |
| 328 | C23 | — | 9 | 1 | no | — |
| 329 | C23 | — | 9 | 3 | no | — |
| 330 | C23 | — | 18 | 1 | no | — |
| 331 | C23 | — | 18 | 3 | no | — |
| 332 | C23 | — | 18 | 3 | no | — |
| 333 | C23 | — | 18 | 6 | no | — |
| 334 | C23 | — | 18 | 3 | no | — |
| 335 | C23 | — | 27 | 1 | no | — |
| 336 | C23 | — | 54 | 3 | no | — |
| 337 | C23 | — | 54 | 3 | no | — |
| 338 | D4 | — | 18 | 3 | no | — |
| 339 | D4 | — | 18 | 3 | no | — |
| 340 | D4 | — | 54 | 3 | no | — |
| 341 | D4 | — | 54 | 3 | no | — |
| 342 | D4 | — | 54 | 3 | no | — |
| 343 | D4 | — | 54 | 3 | no | — |
| 344 | D4 | — | 54 | 3 | no | — |
| 345 | D4 | — | 54 | 3 | no | — |
| 346 | C2×C4 | — | 9 | 3 | no | — |
| 347 | C2×C4 | — | 27 | 3 | no | — |
| 348 | C2×C4 | — | 54 | 3 | no | — |
| 349 | C2×C4 | — | 54 | 3 | no | — |
| 350 | C2×C3 | — | 3 | 3 | no | — |
| 351 | C2×C3 | — | 3 | 3 | no | — |
| 352 | C2×C3 | — | 3 | 1 | no | — |
| 353 | C2×C3 | — | 6 | 3 | no | — |
| 354 | C2×C3 | — | 6 | 1 | no | — |
| 355 | C2×C3 | — | 6 | 1 | no | — |
| 356 | C2×C3 | — | 9 | 3 | no | — |
| 357 | C2×C3 | — | 12 | 1 | no | — |
| 358 | C2×C3 | — | 18 | 1 | no | — |
| 359 | C2×C3 | — | 36 | 1 | no | — |
| 360 | D3 | — | 3 | 3 | no | — |
| 361 | D3 | — | 6 | 1 | no | — |
| 362 | D3 | — | 12 | 1 | no | — |
| 363 | D3 | — | 36 | 1 | no | — |
| 364 | D3 | — | 36 | 1 | no | — |
| 365 | D3 | — | 72 | 1 | no | — |
| 366 | D3 | #64188 | 1 | 1 | yes | characteristic, direct product factor |
| 367 | C22 | — | 2 | 1 | no | — |
| 368 | C22 | — | 3 | 1 | no | — |
| 369 | C22 | — | 3 | 3 | no | — |
| 370 | C22 | — | 6 | 3 | no | — |
| 371 | C22 | — | 9 | 3 | no | — |
| 372 | C22 | — | 9 | 3 | no | — |
| 373 | C22 | — | 9 | 3 | no | — |
| 374 | C22 | — | 9 | 3 | no | — |
| 375 | C22 | — | 18 | 1 | no | — |
| 376 | C22 | — | 18 | 6 | no | — |
| 377 | C22 | — | 18 | 3 | no | — |
| 378 | C22 | — | 18 | 3 | no | — |
| 379 | C22 | — | 18 | 3 | no | — |
| 380 | C22 | — | 18 | 1 | no | — |
| 381 | C22 | — | 54 | 3 | no | — |
| 382 | C22 | — | 108 | 1 | no | — |
| 383 | C22 | — | 108 | 3 | no | — |
| 384 | C22 | D3×(C22⋊C9)⋊C2 | 1 | 3 | yes | complemented |
| 385 | C4 | — | 18 | 3 | no | — |
| 386 | C4 | — | 54 | 3 | no | — |
| 387 | C3 | — | 2 | 1 | no | — |
| 388 | C3 | C2×#64188 | 1 | 1 | yes | characteristic, complemented |
| 389 | C3 | D3×#1020 | 1 | 1 | yes | characteristic |
| 390 | C2 | — | 3 | 3 | no | — |
| 391 | C2 | — | 3 | 1 | no | — |
| 392 | C2 | — | 6 | 1 | no | — |
| 393 | C2 | — | 9 | 3 | no | — |
| 394 | C2 | — | 18 | 1 | no | — |
| 395 | C2 | — | 36 | 1 | no | — |
| 396 | C2 | — | 108 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C22⋊(C22⋊C9) | C22 |
| Frattini | C3 | D3×#1020 |
| Fitting, socle | C24×C32 | C2×D3 |
| LCS | G ▷ C3×C22⋊(C22⋊C9) | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×C22⋊(C22⋊C9) | C2 | semidirect |
| 2. C3⋊#64188 | C2 | semidirect |
| 3. C3×#64188 | C2 | semidirect |
| 6. C3×C22⋊(C22⋊C9) | C22 | semidirect |
| 13. #64188 | D3 | direct (N × H) |
| 41. C22⋊(C22⋊C9) | C2×D3 | semidirect |
| 50. C24×D3 | D9 | semidirect |
| 108. C24×C3 | C2×D9 | semidirect |
| 213. C22×D3 | (C22⋊C9)⋊C2 | semidirect |
| 257. C24 | D3×D9 | semidirect |
| 293. C22×C3 | C2×(C22⋊C9)⋊C2 | semidirect |
| 366. D3 | #64188 | direct (N × H) |
| 384. C22 | D3×(C22⋊C9)⋊C2 | semidirect |
| 388. C3 | C2×#64188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C22⋊(C22⋊C9) | 2 |
| C3⋊#64188 | 2 |
| C3×#64188 | 2 |
| C2×#64188 | 3 |
| D3×#953 | 3 |
| D3×(C22⋊C9)⋊C2 | 4 |