Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 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 |
|---|---|---|
| 3. #70802 | C2 | semidirect |
| 5. #69857 | C2 | semidirect |
| 6. C3×#1300 | C2 | semidirect |
| 7. #67615 | C2 | semidirect |
| 38. #1300 | D3 | semidirect |
| 431. C3 | #9029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79335 | 2 |
| #73419 | 2 |
| #70802 | 2 |
| C4×#823 | 2 |
| #69857 | 2 |
| C3×#1300 | 2 |
| #67615 | 2 |
| #9029 | 3 |