Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
488 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C7×#1518 | C2 | semidirect |
| 4. #11729578 | C2 | semidirect |
| 6. #11725551 | C2 | semidirect |
| 7. #11725437 | C2 | semidirect |
| 12. #89859 | C4 | semidirect |
| 13. #89856 | C4 | semidirect |
| 70. #1518 | D7 | semidirect |
| 322. C7 | #9303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740795 | 2 |
| #11736731 | 2 |
| C7×#1518 | 2 |
| #11729578 | 2 |
| #11727310 | 2 |
| #11725551 | 2 |
| #11725437 | 2 |
| #9303 | 7 |