Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
562 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 167 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. C7×#1744 | C2 | semidirect |
| 4. #11727145 | C2 | semidirect |
| 5. #11725461 | C2 | semidirect |
| 19. #89254 | C4 | semidirect |
| 49. #1744 | D7 | semidirect |
| 253. C7 | #8179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11730744 | 2 |
| C7×#1744 | 2 |
| C2×#89254 | 2 |
| #11727145 | 2 |
| #11725461 | 2 |
| #8179 | 7 |