Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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. #11731604 | C2 | semidirect |
| 5. #11728521 | C2 | semidirect |
| 6. #11725552 | C2 | semidirect |
| 7. #11725437 | C2 | semidirect |
| 14. #89862 | C4 | semidirect |
| 15. #89847 | C4 | semidirect |
| 366. C7 | #9182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740759 | 2 |
| #11731604 | 2 |
| C7×#1517 | 2 |
| #11729565 | 2 |
| #11728521 | 2 |
| #11725552 | 2 |
| #11725437 | 2 |
| #9182 | 7 |