Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22601328 | C2 | semidirect |
| 2. #22590608 | C2 | semidirect |
| 4. #22590402 | C2 | semidirect |
| 6. #22590389 | C2 | semidirect |
| 7. #22590248 | C2 | semidirect |
| 8. #22590203 | C2 | semidirect |
| 9. C4×Q32×C71 | C2 | semidirect |
| 152. C4×Q32 | D71 | semidirect |
| 153. C71 | #33969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601328 | 2 |
| #22590608 | 2 |
| #22590601 | 2 |
| #22590402 | 2 |
| #22590398 | 2 |
| #22590389 | 2 |
| #22590248 | 2 |
| #22590203 | 2 |
| C4×Q32×C71 | 2 |
| #33969 | 71 |