Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 12. #4699 | C4 | semidirect |
| 14. C4×Dic12 | C4 | semidirect |
| 15. #4682 | C4 | semidirect |
| 230. C3 | #11745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78475 | 2 |
| C3×#2163 | 2 |
| C4×#817 | 2 |
| #67528 | 2 |
| #11745 | 3 |