Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 15. #89317 | C4 | semidirect |
| 150. C7 | #13653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×Q32 | 2 |
| C2×#89317 | 2 |
| C4×Dic56 | 2 |
| #11725632 | 2 |
| #11725384 | 2 |
| #11725382 | 2 |
| #11725314 | 2 |
| #13653 | 7 |