Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. #11736711 | C2 | semidirect |
| 3. #11728574 | C2 | semidirect |
| 6. C7×#1287 | C2 | semidirect |
| 7. #11725561 | C2 | semidirect |
| 77. #1287 | D7 | semidirect |
| 296. C7 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736764 | 2 |
| #11736711 | 2 |
| #11728574 | 2 |
| #11728565 | 2 |
| #11728512 | 2 |
| C7×#1287 | 2 |
| #11725561 | 2 |
| #9372 | 7 |