Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
398 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11731720 | C2 | semidirect |
| 5. #11725555 | C2 | semidirect |
| 6. #11725554 | C2 | semidirect |
| 7. #11725439 | C2 | semidirect |
| 30. C7×C4⋊Q8 | Q8 | semidirect |
| 31. C7×#127 | Q8 | semidirect |
| 184. C4⋊Q8 | Dic14 | semidirect |
| 185. #127 | Dic14 | semidirect |
| 335. C7 | #10378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11731720 | 2 |
| C7×#1514 | 2 |
| #11729572 | 2 |
| #11729566 | 2 |
| #11725555 | 2 |
| #11725554 | 2 |
| #11725439 | 2 |
| #10378 | 7 |