Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #11728278 | C2 | semidirect |
| 4. #11728261 | C2 | semidirect |
| 6. C7×#1309 | C2 | semidirect |
| 7. #11725516 | C2 | semidirect |
| 80. #1309 | D7 | semidirect |
| 345. C7 | #9353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736502 | 2 |
| #11736496 | 2 |
| #11728278 | 2 |
| #11728261 | 2 |
| #11728251 | 2 |
| C7×#1309 | 2 |
| #11725516 | 2 |
| #9353 | 7 |