Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
322 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 322 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×C4×M32 | C2 | semidirect |
| 3. #69732 | C2 | semidirect |
| 4. #67517 | C2 | semidirect |
| 5. #67516 | C2 | semidirect |
| 25. C4×M32 | D3 | semidirect |
| 269. C3 | #11682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78469 | 2 |
| C3×C4×M32 | 2 |
| #69732 | 2 |
| #67517 | 2 |
| #67516 | 2 |
| #11682 | 3 |