Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×#14524074 | C2 | semidirect |
| 2. C2×#14524050 | C2 | semidirect |
| 4. #16863652 | C2 | semidirect |
| 5. #16863644 | C2 | semidirect |
| 6. #16863635 | C2 | semidirect |
| 7. #16863627 | C2 | semidirect |
| 8. #16863439 | C2 | semidirect |
| 9. #16863390 | C2 | semidirect |
| 10. C2×#14523967 | C2 | semidirect |
| 11. #536×C67 | C2 | semidirect |
| 54. #11761612 | D4 | semidirect |
| 144. C67 | #3063 | semidirect |
| 148. #536 | D67 | semidirect |