Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
786 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 95 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. C4×#6408 | C2 | semidirect |
| 3. #11729357 | C2 | semidirect |
| 4. #11725451 | C2 | semidirect |
| 5. C23×C7×D4 | C4 | semidirect |
| 9. C7×#394 | C4 | semidirect |
| 12. C7×#380 | C4 | semidirect |
| 17. #89321 | C22 | semidirect |
| 19. #89320 | C22 | semidirect |
| 106. C23×D4 | Dic7 | semidirect |
| 112. #394 | Dic7 | semidirect |
| 115. #380 | Dic7 | semidirect |
| 345. C7 | #11772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2408 | 2 |
| C4×#6408 | 2 |
| #11729357 | 2 |
| #11725451 | 2 |
| #11772 | 7 |