Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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×#2253 | C2 | semidirect |
| 4. #11725385 | C2 | semidirect |
| 5. #11725316 | C2 | semidirect |
| 30. #2253 | D7 | semidirect |
| 122. C7 | #13709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2253 | 2 |
| #11726821 | 2 |
| #11725386 | 2 |
| #11725385 | 2 |
| #11725316 | 2 |
| #13709 | 7 |