Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 99 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×#1757 | C2 | semidirect |
| 3. #11729768 | C2 | semidirect |
| 4. #11727903 | C2 | semidirect |
| 5. #11727811 | C2 | semidirect |
| 8. C22×D56 | C4 | semidirect |
| 15. #89903 | C4 | semidirect |
| 19. #89878 | C4 | semidirect |
| 67. #1757 | D7 | semidirect |
| 308. C7 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741244 | 2 |
| C7×#1757 | 2 |
| #11729768 | 2 |
| #11727903 | 2 |
| #11727811 | 2 |
| #13234 | 7 |