Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
910 conjugacy classes of subgroups; only the 363 normal subgroups are shown.
This group has 910 conjugacy classes of subgroups — too many to draw. Only its 363 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 |
|---|---|---|
| 44. C7×#97 | Q8 | semidirect |
| 117. C7×C8 | C4⋊Q8 | semidirect |
| 140. #97 | Dic14 | semidirect |
| 204. C8 | #6432 | semidirect |
| 205. C7 | #33314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89454 | 2 |
| C2×#89452 | 2 |
| #11730756 | 2 |
| #11730753 | 2 |
| C4×C7×#97 | 2 |
| #11727570 | 2 |
| #33314 | 7 |