Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
462 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 462 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. #78573 | C2 | semidirect |
| 5. #70654 | C2 | semidirect |
| 6. #67725 | C2 | semidirect |
| 7. #67672 | C2 | semidirect |
| 18. C2×#829 | C4 | semidirect |
| 19. C2×#827 | C4 | semidirect |
| 329. C3 | #13034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5195 | 2 |
| #78573 | 2 |
| C3×#1976 | 2 |
| #72076 | 2 |
| #70654 | 2 |
| #67725 | 2 |
| #67672 | 2 |
| #13034 | 3 |