Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
318 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 39. C7×M32 | Q8 | semidirect |
| 43. C2×C7×C16 | Q8 | semidirect |
| 47. #6393 | Q8 | semidirect |
| 151. M32 | Dic14 | semidirect |
| 155. C2×C16 | Dic14 | semidirect |
| 246. C7 | #13455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735991 | 2 |
| #11729182 | 2 |
| C2×#89299 | 2 |
| #11727648 | 2 |
| C7×#1379 | 2 |
| #11725623 | 2 |
| #11725613 | 2 |
| #13455 | 7 |