Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 35. C7×M32 | Q8 | semidirect |
| 47. #6391 | Q8 | semidirect |
| 135. M32 | Dic14 | semidirect |
| 222. C7 | #13454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735924 | 2 |
| #11729182 | 2 |
| #11727574 | 2 |
| C7×#1377 | 2 |
| #11725625 | 2 |
| #13454 | 7 |