Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1188 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1188 conjugacy classes of subgroups — too many to draw. Only its 311 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. #84119 | C2 | semidirect |
| 3. #71871 | C2 | semidirect |
| 4. #71819 | C2 | semidirect |
| 6. C2×C3×2−1+4 | C4 | semidirect |
| 10. C3×#536 | C4 | semidirect |
| 13. C2×C3×C4⋊Q8 | C4 | semidirect |
| 14. C3×C4×#41 | C4 | semidirect |
| 56. C2×2−1+4 | Dic3 | semidirect |
| 60. #536 | Dic3 | semidirect |
| 63. C2×C4⋊Q8 | Dic3 | semidirect |
| 65. C4×#41 | Dic3 | semidirect |
| 265. C3 | #33360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3499 | 2 |
| #84119 | 2 |
| #71871 | 2 |
| #71819 | 2 |
| #33360 | 3 |