Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14524062 | C2 | semidirect |
| 2. C2×D8×D67 | C2 | semidirect |
| 3. #16864041 | C2 | semidirect |
| 4. #16863780 | C2 | semidirect |
| 5. #16863638 | C2 | semidirect |
| 6. #16863633 | C2 | semidirect |
| 7. #16863611 | C2 | semidirect |
| 8. #16863548 | C2 | semidirect |
| 9. #16863542 | C2 | semidirect |
| 10. C8×D268 | C2 | semidirect |
| 11. C4×D8×C67 | C2 | semidirect |
| 12. C2×#11761627 | C22 | semidirect |
| 15. C2×Dic268 | C22 | semidirect |
| 16. C2×#11761617 | C22 | semidirect |
| 17. C2×#11761616 | C22 | semidirect |
| 22. C2×C8×D67 | C22 | semidirect |
| 23. #14524031 | C22 | semidirect |
| 26. #14524018 | C22 | semidirect |
| 31. C4⋊(C67⋊C8) | C22 | semidirect |
| 32. #14523966 | C22 | semidirect |
| 33. #14523963 | C22 | semidirect |
| 35. (C2×D67)⋊C8 | C22 | semidirect |
| 37. C4×D4×C67 | C22 | semidirect |
| 38. #107×C67 | C22 | semidirect |
| 39. #102×C67 | C22 | semidirect |
| 40. C4×C8×C67 | C22 | semidirect |
| 74. D8×C67 | D4 | semidirect |
| 127. C2×D67 | #135 | semidirect |
| 144. C67 | #3280 | semidirect |
| 154. C4×D8 | D67 | semidirect |
| 175. C4×D4 | C2×D67 | semidirect |
| 177. #107 | C2×D67 | semidirect |
| 181. #102 | C2×D67 | semidirect |
| 184. C4×C8 | C2×D67 | semidirect |
| 206. D8 | D268 | semidirect |