Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 2. #16863770 | C2 | semidirect |
| 3. #16863744 | C2 | semidirect |
| 4. #16863596 | C2 | semidirect |
| 5. #16863546 | C2 | semidirect |
| 6. #16863449 | C2 | semidirect |
| 7. #533×C67 | C2 | semidirect |
| 11. C2×#11761615 | C22 | semidirect |
| 16. C4⋊(C67⋊C8) | C22 | semidirect |
| 17. #14523963 | C22 | semidirect |
| 19. C4×C67⋊C8 | C22 | semidirect |
| 20. C4⋊Q8×C67 | C22 | semidirect |
| 21. C4⋊Q8×C67 | C22 | semidirect |
| 26. C4×Q8×C67 | C22 | semidirect |
| 69. C2×C4×C67 | SD16 | semidirect |
| 105. C67 | #3208 | semidirect |
| 106. #533 | D67 | semidirect |
| 117. C4⋊Q8 | C2×D67 | semidirect |
| 118. C4⋊Q8 | C2×D67 | semidirect |
| 127. C4×Q8 | C2×D67 | semidirect |
| 180. C2×C4 | #11761615 | semidirect |