Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
508 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11730833 | C2 | semidirect |
| 4. #11728532 | C2 | semidirect |
| 6. C7×#1274 | C2 | semidirect |
| 7. #11725544 | C2 | semidirect |
| 21. #89466 | C4 | semidirect |
| 22. #89454 | C4 | semidirect |
| 75. #1274 | D7 | semidirect |
| 347. C7 | #9300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736713 | 2 |
| #11730833 | 2 |
| #11728544 | 2 |
| #11728532 | 2 |
| #11727194 | 2 |
| C7×#1274 | 2 |
| #11725544 | 2 |
| #9300 | 7 |