Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×Dic268 | C2 | semidirect |
| 3. #16863839 | C2 | direct (N × H) |
| 4. C2×Dic536 | C2 | semidirect |
| 5. C2×#14523988 | C2 | semidirect |
| 6. C2×M32×C67 | C2 | semidirect |
| 15. C2×Dic268 | C22 | semidirect |
| 18. Dic536 | C22 | semidirect |
| 19. #14523988 | C22 | semidirect |
| 21. M32×C67 | C22 | semidirect |
| 80. C2×C67 | #510 | semidirect |
| 84. C67 | C2×#510 | semidirect |
| 90. C2×M32 | D67 | semidirect |
| 105. M32 | C2×D67 | semidirect |
| 165. C2 | #16863839 | direct (N × H) |