Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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. C7×#3163 | C2 | semidirect |
| 5. #11725531 | C2 | semidirect |
| 6. #11725527 | C2 | semidirect |
| 7. #11725478 | C2 | semidirect |
| 38. C2×Dic28 | Q8 | semidirect |
| 43. C2×D56 | Q8 | semidirect |
| 64. #3163 | D7 | semidirect |
| 291. C7 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3163 | 2 |
| #11728410 | 2 |
| C2×#89283 | 2 |
| #11727651 | 2 |
| #11725531 | 2 |
| #11725527 | 2 |
| #11725478 | 2 |
| #13374 | 7 |