Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 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 |
|---|---|---|
| 1. C2×#14524066 | C2 | semidirect |
| 2. C22×C8×D67 | C2 | semidirect |
| 3. #16863909 | C2 | semidirect |
| 4. #16863634 | C2 | semidirect |
| 5. #16863633 | C2 | semidirect |
| 6. #16863632 | C2 | semidirect |
| 7. #16863628 | C2 | semidirect |
| 8. #16863627 | C2 | semidirect |
| 9. #16863433 | C2 | semidirect |
| 10. #16863391 | C2 | semidirect |
| 11. #467×C67 | C2 | semidirect |
| 15. C2×#11761615 | C22 | semidirect |
| 16. C2×D536 | C22 | semidirect |
| 31. #14523977 | C22 | semidirect |
| 32. #14523974 | C22 | semidirect |
| 33. #14523967 | C22 | semidirect |
| 34. #14523965 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 36. C2×Q16×C67 | C22 | semidirect |
| 39. #107×C67 | C22 | semidirect |
| 40. #103×C67 | C22 | semidirect |
| 64. C8×D67 | D4 | semidirect |
| 118. C22×C67 | #135 | semidirect |
| 129. C2×D67 | #135 | semidirect |
| 146. C67 | #3050 | semidirect |
| 151. #467 | D67 | semidirect |
| 161. C2×Q16 | C2×D67 | semidirect |
| 181. #107 | C2×D67 | semidirect |
| 184. #103 | C2×D67 | semidirect |
| 274. C22 | #14524066 | semidirect |