Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 200 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. C7×#2264 | C2 | semidirect |
| 2. #11729265 | C2 | semidirect |
| 4. #11729254 | C2 | semidirect |
| 5. #11725633 | C2 | semidirect |
| 6. #11725410 | C2 | semidirect |
| 7. #11725405 | C2 | semidirect |
| 45. #2264 | D7 | semidirect |
| 179. C7 | #13691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2264 | 2 |
| #11729265 | 2 |
| #11729263 | 2 |
| #11729254 | 2 |
| #11725633 | 2 |
| #11725410 | 2 |
| #11725405 | 2 |
| #13691 | 7 |