Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11729107 | C2 | semidirect |
| 5. #11725606 | C2 | semidirect |
| 6. #11725378 | C2 | semidirect |
| 7. #11725373 | C2 | semidirect |
| 173. C7 | #12466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2231 | 2 |
| #11729107 | 2 |
| #11728681 | 2 |
| #11728678 | 2 |
| #11725606 | 2 |
| #11725378 | 2 |
| #11725373 | 2 |
| #12466 | 7 |