Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. C7×#2981 | C2 | semidirect |
| 3. #11729566 | C2 | semidirect |
| 4. #11728586 | C2 | semidirect |
| 5. #11728519 | C2 | semidirect |
| 6. #11725563 | C2 | semidirect |
| 7. #11725543 | C2 | semidirect |
| 16. #89865 | C4 | semidirect |
| 17. #89860 | C4 | semidirect |
| 18. #89848 | C4 | semidirect |
| 19. #89845 | C4 | semidirect |
| 73. #2981 | D7 | semidirect |
| 330. C7 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2981 | 2 |
| #11740749 | 2 |
| #11729566 | 2 |
| #11728586 | 2 |
| #11728519 | 2 |
| #11725563 | 2 |
| #11725543 | 2 |
| #9281 | 7 |