Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
448 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. C7×#1813 | C2 | semidirect |
| 3. #11729765 | C2 | semidirect |
| 4. #11727904 | C2 | semidirect |
| 6. #11727901 | C2 | semidirect |
| 11. C22×#1132 | C4 | semidirect |
| 19. #89903 | C4 | semidirect |
| 20. #89892 | C4 | semidirect |
| 23. #89878 | C4 | semidirect |
| 88. #1813 | D7 | semidirect |
| 394. C7 | #13232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741243 | 2 |
| C7×#1813 | 2 |
| #11729765 | 2 |
| #11727904 | 2 |
| #11727903 | 2 |
| #11727901 | 2 |
| #11727900 | 2 |
| #13232 | 7 |