Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 45. C7×M32 | Q8 | semidirect |
| 51. C7×#106 | Q8 | semidirect |
| 61. #6386 | Q8 | semidirect |
| 179. M32 | Dic14 | semidirect |
| 195. #106 | Dic14 | semidirect |
| 288. C7 | #13454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736616 | 2 |
| #11729182 | 2 |
| #11728403 | 2 |
| #11728316 | 2 |
| C7×#1386 | 2 |
| #11725618 | 2 |
| #11725527 | 2 |
| #13454 | 7 |