Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
636 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. #82028 | C2 | semidirect |
| 2. #81808 | C2 | semidirect |
| 3. C3×#2247 | C2 | semidirect |
| 4. #71507 | C2 | semidirect |
| 5. #71506 | C2 | semidirect |
| 6. #71317 | C2 | semidirect |
| 7. #69067 | C2 | semidirect |
| 8. #69056 | C2 | semidirect |
| 34. #2247 | D3 | semidirect |
| 272. C3 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82028 | 2 |
| #81808 | 2 |
| C3×#2247 | 2 |
| #71507 | 2 |
| #71506 | 2 |
| #71317 | 2 |
| #69067 | 2 |
| #69056 | 2 |
| #33860 | 3 |