Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
378 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #11735991 | C2 | semidirect |
| 5. #11725538 | C2 | semidirect |
| 6. #11725535 | C2 | semidirect |
| 7. #11725477 | C2 | semidirect |
| 32. C2×C7×D8 | Q8 | semidirect |
| 164. C2×D8 | Dic14 | semidirect |
| 291. C7 | #13369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735991 | 2 |
| C7×#1978 | 2 |
| #11729787 | 2 |
| C2×#89357 | 2 |
| #11725538 | 2 |
| #11725535 | 2 |
| #11725477 | 2 |
| #13369 | 7 |