Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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×#2158 | C2 | semidirect |
| 5. #11725613 | C2 | semidirect |
| 6. #11725533 | C2 | semidirect |
| 7. #11725531 | C2 | semidirect |
| 54. #2158 | D7 | semidirect |
| 251. C7 | #13500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2158 | 2 |
| C2×#89303 | 2 |
| #11728419 | 2 |
| #11728418 | 2 |
| #11725613 | 2 |
| #11725533 | 2 |
| #11725531 | 2 |
| #13500 | 7 |