Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
554 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #70823 | C2 | semidirect |
| 5. #70822 | C2 | semidirect |
| 6. C3×#1285 | C2 | semidirect |
| 7. #67621 | C2 | semidirect |
| 36. #1285 | D3 | semidirect |
| 385. C3 | #9455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79335 | 2 |
| #73800 | 2 |
| #70827 | 2 |
| #70823 | 2 |
| #70822 | 2 |
| C3×#1285 | 2 |
| #67621 | 2 |
| #9455 | 3 |