Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
196 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 51 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. #11729253 | C2 | semidirect |
| 5. C7×#1420 | C2 | semidirect |
| 6. #11725405 | C2 | semidirect |
| 7. #11725390 | C2 | semidirect |
| 51. #1420 | D7 | semidirect |
| 177. C7 | #13693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729253 | 2 |
| #11729247 | 2 |
| #11727128 | 2 |
| #11727111 | 2 |
| C7×#1420 | 2 |
| #11725405 | 2 |
| #11725390 | 2 |
| #13693 | 7 |