Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11736710 | C2 | semidirect |
| 5. #11727229 | C2 | semidirect |
| 6. #11725548 | C2 | semidirect |
| 7. #11725427 | C2 | semidirect |
| 12. #89863 | C4 | semidirect |
| 13. #89863 | C4 | semidirect |
| 14. #89847 | C4 | semidirect |
| 15. #89847 | C4 | semidirect |
| 379. C7 | #9164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740761 | 2 |
| #11736710 | 2 |
| C7×#1502 | 2 |
| #11729552 | 2 |
| #11727229 | 2 |
| #11725548 | 2 |
| #11725427 | 2 |
| #9164 | 7 |