Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 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. #11735936 | C2 | semidirect |
| 3. C7×#1961 | C2 | semidirect |
| 4. #11729513 | C2 | semidirect |
| 5. #11727299 | C2 | semidirect |
| 6. #11725466 | C2 | semidirect |
| 7. #11725437 | C2 | semidirect |
| 17. #89845 | C4 | semidirect |
| 19. #89842 | C4 | semidirect |
| 71. #1961 | D7 | semidirect |
| 108. C2×C7×C8 | D8 | semidirect |
| 296. C2×C8 | #1141 | semidirect |
| 360. C7 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740611 | 2 |
| #11735936 | 2 |
| C7×#1961 | 2 |
| #11729513 | 2 |
| #11727299 | 2 |
| #11725466 | 2 |
| #11725437 | 2 |
| #9293 | 7 |