Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
574 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11736708 | C2 | semidirect |
| 4. #11728282 | C2 | semidirect |
| 6. C7×#1303 | C2 | semidirect |
| 7. #11725426 | C2 | semidirect |
| 71. #1303 | D7 | semidirect |
| 335. C7 | #9398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736708 | 2 |
| #11731157 | 2 |
| #11728528 | 2 |
| #11728282 | 2 |
| #11728256 | 2 |
| C7×#1303 | 2 |
| #11725426 | 2 |
| #9398 | 7 |