Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
396 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11736761 | C2 | semidirect |
| 3. #11728567 | C2 | semidirect |
| 6. C7×#1287 | C2 | semidirect |
| 7. #11725546 | C2 | semidirect |
| 77. #1287 | D7 | semidirect |
| 302. C7 | #9284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736761 | 2 |
| #11736715 | 2 |
| #11728567 | 2 |
| #11728560 | 2 |
| #11728555 | 2 |
| C7×#1287 | 2 |
| #11725546 | 2 |
| #9284 | 7 |