Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17986437 | C2 | semidirect |
| 2. #22598061 | C2 | semidirect |
| 3. #22597989 | C2 | semidirect |
| 4. C2×#17985811 | C2 | semidirect |
| 5. #22590075 | C2 | semidirect |
| 6. #22589969 | C2 | semidirect |
| 7. C71×#1389 | C2 | semidirect |
| 43. C2×Dic284 | D4 | semidirect |
| 51. C2×D568 | D4 | semidirect |
| 75. M32×C71 | D4 | semidirect |
| 78. #108×C71 | D4 | semidirect |
| 218. #1389 | D71 | semidirect |
| 219. C71 | #13310 | semidirect |
| 283. M32 | D284 | semidirect |
| 287. #108 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986437 | 2 |
| #22598061 | 2 |
| #22597989 | 2 |
| C2×#17985811 | 2 |
| #22590075 | 2 |
| #22589969 | 2 |
| C71×#1389 | 2 |
| #13310 | 71 |