Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
262 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 19. #89285 | C4 | semidirect |
| 20. #89285 | C4 | semidirect |
| 21. #89284 | C4 | semidirect |
| 22. #89284 | C4 | semidirect |
| 231. C7 | #13113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11728458 | 2 |
| #11728413 | 2 |
| #11728402 | 2 |
| C7×#1382 | 2 |
| #11725613 | 2 |
| #11725610 | 2 |
| #11725534 | 2 |
| #13113 | 7 |