Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1630 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 1630 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 |
|---|---|---|
| 3. C2×#5116 | C2 | semidirect |
| 4. #71972 | C2 | semidirect |
| 5. #71971 | C2 | semidirect |
| 12. C22×Dic12 | C22 | semidirect |
| 17. C2×#818 | C22 | semidirect |
| 18. C2×#816 | C22 | semidirect |
| 19. #4551 | C22 | semidirect |
| 63. C24×C3 | Q16 | semidirect |
| 139. C24 | Dic12 | semidirect |
| 171. C22×C3 | #467 | semidirect |
| 213. C22 | #5116 | semidirect |
| 222. C3 | #32931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C8 | 2 |
| #84031 | 2 |
| C2×#5116 | 2 |
| #71972 | 2 |
| #71971 | 2 |
| #32931 | 3 |