Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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×#1810 | C2 | semidirect |
| 3. #11729724 | C2 | semidirect |
| 5. #11725491 | C2 | semidirect |
| 8. C2×#6464 | C4 | semidirect |
| 15. #89882 | C4 | semidirect |
| 19. #89874 | C4 | semidirect |
| 20. #89873 | C4 | semidirect |
| 66. #1810 | D7 | semidirect |
| 338. C7 | #8626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741179 | 2 |
| C7×#1810 | 2 |
| #11729724 | 2 |
| #11727733 | 2 |
| #11725491 | 2 |
| #8626 | 7 |