Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 105 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. #78561 | C2 | semidirect |
| 3. C3×#1976 | C2 | semidirect |
| 4. #72076 | C2 | semidirect |
| 5. #70652 | C2 | semidirect |
| 6. #67725 | C2 | semidirect |
| 7. #67672 | C2 | semidirect |
| 18. C2×#828 | C4 | semidirect |
| 19. C2×#826 | C4 | semidirect |
| 32. #1976 | D3 | semidirect |
| 41. C2×C3×Q16 | C2×C4 | semidirect |
| 43. C2×C3×D8 | C2×C4 | semidirect |
| 74. C2×C3⋊C16 | C2×C4 | semidirect |
| 148. C2×Q16 | C4×D3 | semidirect |
| 156. C2×D8 | C4×D3 | semidirect |
| 340. C3 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5193 | 2 |
| #78561 | 2 |
| C3×#1976 | 2 |
| #72076 | 2 |
| #70652 | 2 |
| #67725 | 2 |
| #67672 | 2 |
| #13033 | 3 |