Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
512 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #11731063 | C2 | semidirect |
| 5. #11728524 | C2 | semidirect |
| 6. #11725542 | C2 | semidirect |
| 7. #11725426 | C2 | semidirect |
| 14. #89866 | C4 | semidirect |
| 15. #89847 | C4 | semidirect |
| 126. C4×Dic7 | SD16 | semidirect |
| 362. C7 | #9238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740760 | 2 |
| #11731063 | 2 |
| C7×#1502 | 2 |
| #11729569 | 2 |
| #11728524 | 2 |
| #11725542 | 2 |
| #11725426 | 2 |
| #9238 | 7 |