Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11730857 | C2 | semidirect |
| 3. #11727621 | C2 | semidirect |
| 4. #11727609 | C2 | semidirect |
| 5. #11727186 | C2 | semidirect |
| 6. C7×#1300 | C2 | semidirect |
| 7. #11725556 | C2 | semidirect |
| 18. #89615 | C4 | semidirect |
| 19. #89614 | C4 | semidirect |
| 47. #6437 | C2×C4 | semidirect |
| 55. #6432 | C2×C4 | semidirect |
| 56. C7×C4⋊C8 | C2×C4 | semidirect |
| 78. #1300 | D7 | semidirect |
| 185. D28 | #104 | semidirect |
| 222. C4⋊C8 | C4×D7 | semidirect |
| 361. C7 | #9325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736788 | 2 |
| #11730857 | 2 |
| #11727621 | 2 |
| #11727609 | 2 |
| #11727186 | 2 |
| C7×#1300 | 2 |
| #11725556 | 2 |
| #9325 | 7 |