Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
408 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 408 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×#1846 | C2 | semidirect |
| 3. #69726 | C2 | semidirect |
| 4. #69546 | C2 | semidirect |
| 17. #4694 | C4 | semidirect |
| 18. #4681 | C4 | semidirect |
| 23. #1846 | D3 | semidirect |
| 253. C3 | #9758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78463 | 2 |
| C3×#1846 | 2 |
| #69726 | 2 |
| #69546 | 2 |
| #69545 | 2 |
| #9758 | 3 |