Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
496 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #11729823 | C2 | semidirect |
| 4. #11729815 | C2 | semidirect |
| 6. #11725613 | C2 | semidirect |
| 7. #11725611 | C2 | semidirect |
| 13. C2×C7×SD32 | C4 | semidirect |
| 34. C2×C7×Q16 | C2×C4 | semidirect |
| 52. C2×C7×C16 | C2×C4 | semidirect |
| 122. C2×SD32 | Dic7 | semidirect |
| 173. C2×Q16 | C2×Dic7 | semidirect |
| 194. C2×C16 | C2×Dic7 | semidirect |
| 300. C7 | #13019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×SD32 | 2 |
| #11741268 | 2 |
| #11729823 | 2 |
| #11729815 | 2 |
| C2×#89358 | 2 |
| #11725613 | 2 |
| #11725611 | 2 |
| #13019 | 7 |