Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
436 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 111 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×#1451 | C2 | semidirect |
| 3. #70761 | C2 | semidirect |
| 4. #69859 | C2 | semidirect |
| 5. C4×#819 | C2 | semidirect |
| 29. #1451 | D3 | semidirect |
| 263. C3 | #9726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78470 | 2 |
| C3×#1451 | 2 |
| #70761 | 2 |
| #69859 | 2 |
| C4×#819 | 2 |
| #9726 | 3 |