Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
204 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×Dic112 | C2 | semidirect |
| 3. C4×Dic56 | C2 | semidirect |
| 5. C7×C4⋊C32 | C2 | semidirect |
| 6. #11725403 | C2 | semidirect |
| 46. C4⋊C32 | D7 | semidirect |
| 171. C7 | #13690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic112 | 2 |
| C2×#89244 | 2 |
| C4×Dic56 | 2 |
| #11726816 | 2 |
| C7×C4⋊C32 | 2 |
| #11725403 | 2 |
| #11725402 | 2 |
| #13690 | 7 |