Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1538 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 315 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. #82093 | C2 | semidirect |
| 3. #72130 | C2 | semidirect |
| 4. #71686 | C2 | semidirect |
| 8. C2×C3×#123 | C4 | semidirect |
| 10. C2×C3×#120 | C4 | semidirect |
| 13. C2×#834 | C22 | semidirect |
| 14. #5212 | C22 | semidirect |
| 15. C4×#217 | C22 | semidirect |
| 48. C2×#123 | Dic3 | semidirect |
| 50. C2×#120 | Dic3 | semidirect |
| 248. C3 | #21795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#534 | 2 |
| #82093 | 2 |
| #72130 | 2 |
| #71686 | 2 |
| #21795 | 3 |