Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
424 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2967 | C2 | semidirect |
| 3. #11729511 | C2 | semidirect |
| 4. #11728589 | C2 | semidirect |
| 5. #11727607 | C2 | semidirect |
| 6. #11725563 | C2 | semidirect |
| 7. #11725472 | C2 | semidirect |
| 18. #89841 | C4 | semidirect |
| 19. #89839 | C4 | semidirect |
| 20. #89832 | C4 | semidirect |
| 21. #89830 | C4 | semidirect |
| 90. #2967 | D7 | semidirect |
| 381. C7 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2967 | 2 |
| #11740592 | 2 |
| #11729511 | 2 |
| #11728589 | 2 |
| #11727607 | 2 |
| #11725563 | 2 |
| #11725472 | 2 |
| #9370 | 7 |