Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1220 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1220 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. #71861 | C2 | semidirect |
| 4. #71819 | C2 | semidirect |
| 7. C2×C3×H(5,𝔽2) | C4 | semidirect |
| 10. C3×#536 | C4 | semidirect |
| 13. C2×C3×#124 | C4 | semidirect |
| 14. C3×C4×#41 | C4 | semidirect |
| 17. #5240 | C22 | semidirect |
| 18. #4545 | C22 | semidirect |
| 19. #4541 | C22 | semidirect |
| 57. C2×H(5,𝔽2) | Dic3 | semidirect |
| 60. #536 | Dic3 | semidirect |
| 63. C2×#124 | Dic3 | semidirect |
| 65. C4×#41 | Dic3 | semidirect |
| 269. C3 | #33362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3500 | 2 |
| #84119 | 2 |
| #71861 | 2 |
| #71819 | 2 |
| #33362 | 3 |