Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
452 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #11728590 | C2 | semidirect |
| 5. #11727616 | C2 | semidirect |
| 6. #11725560 | C2 | semidirect |
| 7. #11725471 | C2 | semidirect |
| 19. #89803 | C4 | semidirect |
| 21. #89793 | C4 | semidirect |
| 22. #89791 | C4 | semidirect |
| 24. #89780 | C4 | semidirect |
| 363. C7 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2970 | 2 |
| #11739980 | 2 |
| #11729397 | 2 |
| #11728590 | 2 |
| #11727616 | 2 |
| #11725560 | 2 |
| #11725471 | 2 |
| #9159 | 7 |