Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
228 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 31 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 | #22626958 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22626930 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22625886 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | (C2×#10596842)⋊C4 | — | 2 | 1 | no | — |
| 5 | #17989673 | — | 2 | 1 | no | — |
| 6 | #17989654 | C4 | 1 | 1 | yes | characteristic |
| 7 | #17989598 | — | 2 | 1 | no | — |
| 8 | #17989539 | C22 | 1 | 1 | yes | characteristic |
| 9 | #17989459 | — | 2 | 1 | no | — |
| 10 | #100×D73 | C4 | 1 | 1 | yes | characteristic |
| 11 | C22×#10596842 | — | 4 | 1 | no | — |
| 12 | C22⋊#10596842 | — | 4 | 1 | no | — |
| 13 | D4×#64408 | — | 4 | 1 | no | — |
| 14 | D4×#64408 | — | 4 | 1 | no | — |
| 15 | #14556670 | — | 2 | 1 | no | — |
| 16 | C2×C4⋊#64408 | D4 | 1 | 1 | yes | characteristic |
| 17 | C2×C22⋊#64408 | — | 4 | 1 | no | — |
| 18 | C2×C22⋊#64408 | — | 4 | 1 | no | — |
| 19 | C2×C4×#64408 | D4 | 1 | 1 | yes | characteristic |
| 20 | #14556660 | — | 4 | 1 | no | — |
| 21 | #14556659 | — | 4 | 1 | no | — |
| 22 | C2×D4×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | M16×D73 | — | 2 | 1 | no | — |
| 24 | #14556508 | C8 | 1 | 1 | yes | characteristic, complemented |
| 25 | #14556507 | — | 2 | 1 | no | — |
| 26 | #100×C73 | C8 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#10596842 | — | 4 | 2 | no | — |
| 28 | C2×#10596842 | — | 8 | 1 | no | — |
| 29 | C2×#10596842 | — | 8 | 1 | no | — |
| 30 | C2×#10596842 | — | 8 | 1 | no | — |
| 31 | C22×#64408 | — | 2 | 1 | no | — |
| 32 | C22×#64408 | — | 2 | 1 | no | — |
| 33 | C22×#64408 | — | 4 | 1 | no | — |
| 34 | C22×#64408 | — | 4 | 1 | no | — |
| 35 | C4⋊#64408 | — | 2 | 1 | no | — |
| 36 | C4⋊#64408 | — | 2 | 1 | no | — |
| 37 | C4⋊#64408 | — | 4 | 1 | no | — |
| 38 | C22⋊#64408 | — | 4 | 2 | no | — |
| 39 | C22⋊#64408 | — | 4 | 1 | no | — |
| 40 | C22⋊#64408 | — | 8 | 1 | no | — |
| 41 | C22⋊#64408 | — | 8 | 1 | no | — |
| 42 | C4×#64408 | — | 4 | 1 | no | — |
| 43 | C4×#64408 | — | 4 | 1 | no | — |
| 44 | C23×D73 | — | 2 | 1 | no | — |
| 45 | C2×D292 | M16 | 1 | 1 | yes | characteristic |
| 46 | C2×C22⋊D73 | — | 2 | 1 | no | — |
| 47 | D4×D73 | — | 4 | 1 | no | — |
| 48 | D4×D73 | — | 4 | 1 | no | — |
| 49 | C2×C4×D73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 50 | #11924012 | — | 2 | 1 | no | — |
| 51 | #11924011 | — | 4 | 1 | no | — |
| 52 | C8×D73 | — | 4 | 1 | no | — |
| 53 | C2×D4×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 54 | M16×C73 | — | 2 | 1 | no | — |
| 55 | C23×C73 | — | 2 | 1 | no | — |
| 56 | C22×D73 | — | 2 | 1 | no | — |
| 57 | C22×D73 | — | 4 | 1 | no | — |
| 58 | C22×D73 | — | 4 | 1 | no | — |
| 59 | C22×D73 | — | 8 | 1 | no | — |
| 60 | C22×D73 | — | 8 | 1 | no | — |
| 61 | C22×D73 | #99 | 1 | 1 | yes | characteristic |
| 62 | C2×#64408 | — | 2 | 1 | no | — |
| 63 | C2×#64408 | — | 2 | 1 | no | — |
| 64 | C2×#64408 | — | 4 | 1 | no | — |
| 65 | C2×#64408 | — | 4 | 1 | no | — |
| 66 | C2×#64408 | — | 4 | 1 | no | — |
| 67 | C2×#64408 | — | 4 | 1 | no | — |
| 68 | C2×#64408 | — | 4 | 1 | no | — |
| 69 | C2×#64408 | — | 8 | 1 | no | — |
| 70 | C2×#64408 | — | 16 | 1 | no | — |
| 71 | C2×#64408 | — | 16 | 1 | no | — |
| 72 | #10596842 | — | 8 | 2 | no | — |
| 73 | #10596842 | — | 16 | 1 | no | — |
| 74 | D4×C73 | — | 4 | 1 | no | — |
| 75 | C2×C4×C73 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 76 | C22⋊D73 | — | 4 | 2 | no | — |
| 77 | C2×Dic73 | #101 | 1 | 1 | yes | characteristic |
| 78 | D292 | — | 4 | 1 | no | — |
| 79 | C4×D73 | — | 2 | 1 | no | — |
| 80 | C4×D73 | — | 2 | 1 | no | — |
| 81 | C8×C73 | — | 4 | 1 | no | — |
| 82 | #10596831 | — | 4 | 1 | no | — |
| 83 | C22×C73 | — | 4 | 1 | no | — |
| 84 | C22×C73 | — | 8 | 1 | no | — |
| 85 | C22×C73 | #324 | 1 | 1 | yes | characteristic |
| 86 | C2×D73 | — | 2 | 1 | no | — |
| 87 | C2×D73 | — | 2 | 1 | no | — |
| 88 | C2×D73 | — | 4 | 1 | no | — |
| 89 | C2×D73 | — | 8 | 1 | no | — |
| 90 | C2×D73 | — | 8 | 1 | no | — |
| 91 | C2×D73 | — | 8 | 1 | no | — |
| 92 | C2×D73 | — | 16 | 1 | no | — |
| 93 | C2×D73 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 94 | C2×D73 | #352 | 1 | 1 | yes | characteristic |
| 95 | #64408 | — | 4 | 1 | no | — |
| 96 | #64408 | — | 4 | 1 | no | — |
| 97 | #64408 | — | 8 | 1 | no | — |
| 98 | #64408 | — | 8 | 1 | no | — |
| 99 | #64408 | — | 8 | 1 | no | — |
| 100 | C4×C73 | — | 2 | 1 | no | — |
| 101 | Dic73 | — | 2 | 1 | no | — |
| 102 | #7375 | — | 73 | 1 | no | maximal, Sylow |
| 103 | C2×C73 | — | 2 | 1 | no | — |
| 104 | C2×C73 | — | 8 | 1 | no | — |
| 105 | C2×C73 | #1326 | 1 | 1 | yes | characteristic |
| 106 | D73 | — | 2 | 1 | no | — |
| 107 | D73 | — | 8 | 1 | no | — |
| 108 | D73 | #1402 | 1 | 1 | yes | characteristic |
| 109 | D73 | #1403 | 1 | 1 | yes | characteristic |
| 110 | #1856 | — | 73 | 1 | no | — |
| 111 | #1318 | — | 73 | 1 | no | — |
| 112 | #1270 | — | 73 | 1 | no | — |
| 113 | C73 | #7375 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 114 | #518 | — | 73 | 1 | no | — |
| 115 | #428 | — | 146 | 1 | no | — |
| 116 | C2×#100 | — | 73 | 1 | no | — |
| 117 | #390 | — | 73 | 1 | no | — |
| 118 | #339 | — | 146 | 1 | no | — |
| 119 | #336 | — | 146 | 1 | no | — |
| 120 | #324 | — | 146 | 1 | no | — |
| 121 | C22×D4 | — | 73 | 1 | no | — |
| 122 | C2×M16 | — | 146 | 1 | no | — |
| 123 | C22×C8 | — | 292 | 1 | no | — |
| 124 | C4×D4 | — | 292 | 1 | no | — |
| 125 | C4×D4 | — | 292 | 1 | no | — |
| 126 | #117 | — | 146 | 1 | no | — |
| 127 | C2×C4⋊C4 | — | 73 | 1 | no | — |
| 128 | C2×C22⋊C4 | — | 292 | 1 | no | — |
| 129 | C2×C22⋊C4 | — | 292 | 1 | no | — |
| 130 | C2×C42 | — | 73 | 1 | no | — |
| 131 | #107 | — | 292 | 1 | no | — |
| 132 | #106 | — | 292 | 1 | no | — |
| 133 | #100 | — | 73 | 1 | no | — |
| 134 | #100 | — | 146 | 1 | no | — |
| 135 | #100 | #10596842 | 1 | 1 | yes | characteristic, complemented |
| 136 | C22⋊C8 | — | 292 | 1 | no | — |
| 137 | C24 | — | 146 | 1 | no | — |
| 138 | C2×D4 | — | 292 | 1 | no | — |
| 139 | C2×D4 | — | 292 | 1 | no | — |
| 140 | C2×D4 | — | 73 | 1 | no | — |
| 141 | C2×D4 | — | 146 | 1 | no | — |
| 142 | C2×D4 | C2×#10596842 | 1 | 1 | yes | characteristic |
| 143 | C22×C4 | — | 292 | 1 | no | — |
| 144 | C22×C4 | — | 292 | 1 | no | — |
| 145 | C22×C4 | — | 73 | 1 | no | — |
| 146 | C22×C4 | — | 146 | 1 | no | — |
| 147 | C22×C4 | — | 146 | 1 | no | — |
| 148 | M16 | — | 2 | 1 | no | — |
| 149 | M16 | — | 292 | 1 | no | — |
| 150 | M16 | — | 146 | 1 | no | — |
| 151 | C2×C8 | — | 292 | 1 | no | — |
| 152 | C2×C8 | — | 292 | 2 | no | — |
| 153 | C2×C8 | — | 584 | 1 | no | — |
| 154 | C2×C8 | — | 584 | 1 | no | — |
| 155 | C2×C8 | — | 584 | 1 | no | — |
| 156 | C4⋊C4 | — | 292 | 1 | no | — |
| 157 | C4⋊C4 | — | 146 | 1 | no | — |
| 158 | C4⋊C4 | — | 146 | 1 | no | — |
| 159 | C22⋊C4 | — | 292 | 2 | no | — |
| 160 | C22⋊C4 | — | 292 | 1 | no | — |
| 161 | C22⋊C4 | — | 584 | 1 | no | — |
| 162 | C22⋊C4 | — | 584 | 1 | no | — |
| 163 | C42 | — | 292 | 1 | no | — |
| 164 | C42 | — | 292 | 1 | no | — |
| 165 | C23 | — | 2 | 1 | no | — |
| 166 | C23 | — | 292 | 1 | no | — |
| 167 | C23 | — | 292 | 1 | no | — |
| 168 | C23 | — | 584 | 1 | no | — |
| 169 | C23 | — | 584 | 1 | no | — |
| 170 | C23 | — | 73 | 1 | no | — |
| 171 | C23 | — | 146 | 1 | no | — |
| 172 | D4 | — | 4 | 1 | no | — |
| 173 | D4 | — | 292 | 1 | no | — |
| 174 | D4 | — | 292 | 2 | no | — |
| 175 | C2×C4 | — | 292 | 1 | no | — |
| 176 | C2×C4 | — | 292 | 1 | no | — |
| 177 | C2×C4 | — | 292 | 1 | no | — |
| 178 | C2×C4 | — | 292 | 1 | no | — |
| 179 | C2×C4 | — | 292 | 1 | no | — |
| 180 | C2×C4 | — | 584 | 1 | no | — |
| 181 | C2×C4 | — | 73 | 1 | no | — |
| 182 | C2×C4 | — | 1168 | 1 | no | — |
| 183 | C2×C4 | — | 1168 | 1 | no | — |
| 184 | C2×C4 | — | 146 | 1 | no | — |
| 185 | C2×C4 | — | 146 | 1 | no | — |
| 186 | C2×C4 | — | 146 | 1 | no | — |
| 187 | C2×C4 | — | 146 | 1 | no | — |
| 188 | C2×C4 | C22⋊#10596842 | 1 | 1 | yes | characteristic |
| 189 | C8 | — | 4 | 1 | no | — |
| 190 | C8 | — | 292 | 1 | no | — |
| 191 | C8 | — | 584 | 2 | no | — |
| 192 | C8 | — | 1168 | 1 | no | — |
| 193 | C22 | — | 4 | 1 | no | — |
| 194 | C22 | — | 8 | 1 | no | — |
| 195 | C22 | — | 292 | 1 | no | — |
| 196 | C22 | — | 584 | 1 | no | — |
| 197 | C22 | — | 584 | 1 | no | — |
| 198 | C22 | — | 584 | 1 | no | — |
| 199 | C22 | — | 73 | 1 | no | — |
| 200 | C22 | — | 73 | 1 | no | — |
| 201 | C22 | — | 1168 | 1 | no | — |
| 202 | C22 | — | 146 | 1 | no | — |
| 203 | C22 | — | 146 | 1 | no | — |
| 204 | C22 | #17989673 | 1 | 1 | yes | characteristic |
| 205 | C4 | — | 2 | 1 | no | — |
| 206 | C4 | — | 292 | 1 | no | — |
| 207 | C4 | — | 292 | 1 | no | — |
| 208 | C4 | — | 584 | 1 | no | — |
| 209 | C4 | — | 584 | 1 | no | — |
| 210 | C4 | — | 584 | 1 | no | — |
| 211 | C4 | — | 146 | 1 | no | — |
| 212 | C2 | — | 2 | 1 | no | — |
| 213 | C2 | — | 8 | 1 | no | — |
| 214 | C2 | — | 584 | 1 | no | — |
| 215 | C2 | — | 73 | 1 | no | — |
| 216 | C2 | — | 73 | 1 | no | — |
| 217 | C2 | — | 146 | 1 | no | — |
| 218 | C2 | #22626969 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 24. #14556508 | C8 | semidirect |
| 26. #100×C73 | C8 | semidirect |
| 113. C73 | #7375 | semidirect |
| 135. #100 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626958 | 2 |
| #22626930 | 2 |
| #22625886 | 2 |
| #7375 | 73 |