Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
278 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11728452 | C2 | semidirect |
| 5. #11725624 | C2 | semidirect |
| 6. #11725621 | C2 | semidirect |
| 7. #11725535 | C2 | semidirect |
| 253. C7 | #13489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2148 | 2 |
| #11729840 | 2 |
| #11729831 | 2 |
| #11728452 | 2 |
| #11725624 | 2 |
| #11725621 | 2 |
| #11725535 | 2 |
| #13489 | 7 |