Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
464 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11727708 | C2 | semidirect |
| 5. #11727677 | C2 | semidirect |
| 6. #11727270 | C2 | semidirect |
| 7. #11725432 | C2 | semidirect |
| 394. C7 | #10562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740076 | 2 |
| C7×#1519 | 2 |
| #11729437 | 2 |
| #11727708 | 2 |
| #11727677 | 2 |
| #11727270 | 2 |
| #11725432 | 2 |
| #10562 | 7 |