Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
640 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 131 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×#2972 | C2 | semidirect |
| 3. #11729373 | C2 | semidirect |
| 4. #11727698 | C2 | semidirect |
| 5. #11725481 | C2 | semidirect |
| 17. #89763 | C4 | semidirect |
| 18. #89755 | C4 | semidirect |
| 19. #89732 | C4 | semidirect |
| 21. #89725 | C4 | semidirect |
| 57. C7×C22⋊C8 | D4 | semidirect |
| 66. #2972 | D7 | semidirect |
| 232. C22⋊C8 | C22⋊D7 | semidirect |
| 393. C7 | #9384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2972 | 2 |
| #11739825 | 2 |
| #11729373 | 2 |
| #11727698 | 2 |
| #11725481 | 2 |
| #9384 | 7 |