Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×#14523983 | C2 | semidirect |
| 3. #16863205 | C2 | semidirect |
| 4. #427×C67 | C2 | semidirect |
| 8. #14524065 | C4 | semidirect |
| 10. C2×Dic268 | C4 | semidirect |
| 12. C2×D536 | C4 | semidirect |
| 14. #14523983 | C22 | semidirect |
| 19. #106×C67 | C22 | semidirect |
| 85. C67 | #2145 | semidirect |
| 88. #427 | D67 | semidirect |
| 104. #106 | C2×D67 | semidirect |