Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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. #16863406 | C2 | semidirect |
| 4. #16863404 | C2 | semidirect |
| 6. #16863152 | C2 | semidirect |
| 7. H(3,ℤ/4)×C67 | C2 | semidirect |
| 14. #14524043 | C4 | semidirect |
| 15. #14524031 | C4 | semidirect |
| 110. C67 | #1909 | semidirect |
| 117. H(3,ℤ/4) | D67 | semidirect |