Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
452 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 89 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. #79054 | C2 | semidirect |
| 3. C3×#1963 | C2 | semidirect |
| 4. #71803 | C2 | semidirect |
| 5. #69431 | C2 | semidirect |
| 6. #67710 | C2 | semidirect |
| 7. #67615 | C2 | semidirect |
| 17. #5089 | C4 | semidirect |
| 18. #5081 | C4 | semidirect |
| 19. #5074 | C4 | semidirect |
| 20. #5071 | C4 | semidirect |
| 38. #1963 | D3 | semidirect |
| 424. C3 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83292 | 2 |
| #79054 | 2 |
| C3×#1963 | 2 |
| #71803 | 2 |
| #69431 | 2 |
| #67710 | 2 |
| #67615 | 2 |
| #8997 | 3 |