Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
430 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 99 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. C3×#1952 | C2 | semidirect |
| 4. C2×#4496 | C2 | semidirect |
| 5. C2×#4492 | C2 | semidirect |
| 7. #67671 | C2 | semidirect |
| 33. #1952 | D3 | semidirect |
| 354. C3 | #13412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78576 | 2 |
| C3×#1952 | 2 |
| C2×#4497 | 2 |
| C2×#4496 | 2 |
| C2×#4492 | 2 |
| #70598 | 2 |
| #67671 | 2 |
| #13412 | 3 |