Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#14524066 | C2 | semidirect |
| 2. C2×D8×D67 | C2 | semidirect |
| 3. #16863833 | C2 | direct (N × H) |
| 4. C2×#14523986 | C2 | semidirect |
| 5. C2×D1072 | C2 | semidirect |
| 6. C2×#14523984 | C2 | semidirect |
| 7. C2×#14523982 | C2 | semidirect |
| 8. C2×SD32×C67 | C2 | semidirect |
| 12. #14524066 | C22 | semidirect |
| 15. C2×D536 | C22 | semidirect |
| 18. D8×D67 | C22 | semidirect |
| 20. #14523986 | C22 | semidirect |
| 21. D1072 | C22 | semidirect |
| 22. #14523984 | C22 | semidirect |
| 23. #14523982 | C22 | semidirect |
| 24. C2×C67⋊C16 | C22 | semidirect |
| 25. C2×Q16×C67 | C22 | semidirect |
| 27. SD32×C67 | C22 | semidirect |
| 28. C2×C16×C67 | C22 | semidirect |
| 44. D536 | C23 | semidirect |
| 49. C67⋊C16 | C23 | semidirect |
| 53. Q16×C67 | C23 | semidirect |
| 57. C16×C67 | C23 | semidirect |
| 98. C2×C67 | #509 | semidirect |
| 104. C67 | C2×#509 | semidirect |
| 109. C2×SD32 | D67 | semidirect |
| 117. C2×Q16 | C2×D67 | semidirect |
| 127. SD32 | C2×D67 | semidirect |
| 132. C2×C16 | C2×D67 | semidirect |
| 147. Q16 | C22×D67 | semidirect |
| 161. C16 | C22×D67 | semidirect |
| 205. C2 | #16863833 | direct (N × H) |