Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 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×#1960 | C2 | semidirect |
| 4. #11729527 | C2 | semidirect |
| 6. #11725466 | C2 | semidirect |
| 7. #11725437 | C2 | semidirect |
| 16. #89860 | C4 | semidirect |
| 18. #89850 | C4 | semidirect |
| 71. #1960 | D7 | semidirect |
| 337. C7 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740660 | 2 |
| #11735936 | 2 |
| C7×#1960 | 2 |
| #11729527 | 2 |
| #11727299 | 2 |
| #11725466 | 2 |
| #11725437 | 2 |
| #9291 | 7 |