Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
356 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 356 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 |
|---|---|---|
| 36. C7×M32 | Q8 | semidirect |
| 38. C7×#107 | Q8 | semidirect |
| 49. #6386 | Q8 | semidirect |
| 140. M32 | Dic14 | semidirect |
| 145. #107 | Dic14 | semidirect |
| 222. C7 | #13457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89627 | 2 |
| C2×#89308 | 2 |
| #11728416 | 2 |
| C2×#89282 | 2 |
| C7×#1386 | 2 |
| #11725616 | 2 |
| #11725532 | 2 |
| #13457 | 7 |