Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. C3×#1567 | C2 | semidirect |
| 3. #70514 | C2 | semidirect |
| 5. #70501 | C2 | semidirect |
| 7. C4×#815 | C2 | semidirect |
| 19. #4694 | C4 | semidirect |
| 20. #4693 | C4 | semidirect |
| 22. #4681 | C4 | semidirect |
| 23. #4680 | C4 | semidirect |
| 32. #1567 | D3 | semidirect |
| 206. C3×C8 | #104 | semidirect |
| 301. C8 | #825 | semidirect |
| 325. C3 | #9851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78468 | 2 |
| C3×#1567 | 2 |
| #70514 | 2 |
| #70512 | 2 |
| #70501 | 2 |
| #70498 | 2 |
| C4×#815 | 2 |
| #9851 | 3 |