Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
478 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 478 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 |
|---|---|---|
| 3. C7×#1993 | C2 | semidirect |
| 4. #11729528 | C2 | semidirect |
| 6. #11725466 | C2 | semidirect |
| 7. #11725437 | C2 | semidirect |
| 14. #89860 | C4 | semidirect |
| 16. #89851 | C4 | semidirect |
| 69. #1993 | D7 | semidirect |
| 321. C7 | #9287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740661 | 2 |
| #11735936 | 2 |
| C7×#1993 | 2 |
| #11729528 | 2 |
| #11727299 | 2 |
| #11725466 | 2 |
| #11725437 | 2 |
| #9287 | 7 |