Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 436 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×#2968 | C2 | semidirect |
| 3. #11729510 | C2 | semidirect |
| 4. #11728544 | C2 | semidirect |
| 5. #11727552 | C2 | semidirect |
| 6. #11725548 | C2 | semidirect |
| 7. #11725465 | C2 | semidirect |
| 18. #89839 | C4 | semidirect |
| 19. #89837 | C4 | semidirect |
| 20. #89830 | C4 | semidirect |
| 21. #89827 | C4 | semidirect |
| 90. #2968 | D7 | semidirect |
| 387. C7 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2968 | 2 |
| #11740582 | 2 |
| #11729510 | 2 |
| #11728544 | 2 |
| #11727552 | 2 |
| #11725548 | 2 |
| #11725465 | 2 |
| #9432 | 7 |