Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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. C7×#1707 | C2 | semidirect |
| 5. #11725607 | C2 | semidirect |
| 6. #11725599 | C2 | semidirect |
| 7. #11725245 | C2 | semidirect |
| 48. #1707 | D7 | semidirect |
| 200. C7 | #12422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1707 | 2 |
| #11729141 | 2 |
| #11729069 | 2 |
| C8×D56 | 2 |
| #11725607 | 2 |
| #11725599 | 2 |
| #11725245 | 2 |
| #12422 | 7 |