Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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×C7×SD64 | C2 | semidirect |
| 2. #11729261 | C2 | semidirect |
| 4. #11727120 | C2 | semidirect |
| 5. #11725633 | C2 | semidirect |
| 6. #11725631 | C2 | semidirect |
| 7. #11725399 | C2 | semidirect |
| 44. C2×SD64 | D7 | semidirect |
| 170. C7 | #13702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×SD64 | 2 |
| #11729261 | 2 |
| #11729226 | 2 |
| #11727120 | 2 |
| #11725633 | 2 |
| #11725631 | 2 |
| #11725399 | 2 |
| #13702 | 7 |