Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
934 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C3×#2972 | C2 | semidirect |
| 3. #71619 | C2 | semidirect |
| 4. #69959 | C2 | semidirect |
| 5. #67676 | C2 | semidirect |
| 19. #4991 | C4 | semidirect |
| 20. #4960 | C4 | semidirect |
| 24. #2972 | D3 | semidirect |
| 40. C22×C3×C8 | D4 | semidirect |
| 149. C22×C8 | #67 | semidirect |
| 181. C23×C3 | #102 | semidirect |
| 215. C2×C3×C4 | #102 | semidirect |
| 340. C23 | #821 | semidirect |
| 371. C2×C4 | #821 | semidirect |
| 419. C3 | #9468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2972 | 2 |
| #82403 | 2 |
| #71619 | 2 |
| #69959 | 2 |
| #67676 | 2 |
| #9468 | 3 |