Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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. C7×#1451 | C2 | semidirect |
| 3. #11728543 | C2 | semidirect |
| 4. #11727621 | C2 | semidirect |
| 5. C4×#6391 | C2 | semidirect |
| 15. #89467 | C4 | semidirect |
| 16. #89466 | C4 | semidirect |
| 19. #89454 | C4 | semidirect |
| 61. #1451 | D7 | semidirect |
| 143. C7×C8 | #104 | semidirect |
| 260. C8 | #6399 | semidirect |
| 261. C7 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735915 | 2 |
| C7×#1451 | 2 |
| #11728543 | 2 |
| #11727621 | 2 |
| C4×#6391 | 2 |
| #9721 | 7 |