Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14524068 | C2 | semidirect |
| 2. C22×#11761613 | C2 | semidirect |
| 3. #16863960 | C2 | semidirect |
| 4. #16863541 | C2 | semidirect |
| 5. #16863530 | C2 | semidirect |
| 6. #16863401 | C2 | semidirect |
| 7. #16863392 | C2 | semidirect |
| 8. #16863363 | C2 | semidirect |
| 9. C2×H(5,𝔽2)×C67 | C2 | semidirect |
| 10. C22×D268 | C22 | semidirect |
| 12. C2×#11761615 | C22 | semidirect |
| 14. C2×#11761613 | C22 | semidirect |
| 15. C2×#11761613 | C22 | semidirect |
| 16. C2×#11761612 | C22 | semidirect |
| 17. C22×C67⋊C8 | C22 | semidirect |
| 20. #14524017 | C22 | semidirect |
| 22. #14524002 | C22 | semidirect |
| 23. #14523967 | C22 | semidirect |
| 24. #14523964 | C22 | semidirect |
| 25. #14523964 | C22 | semidirect |
| 26. C22⋊(C67⋊C8) | C22 | semidirect |
| 32. C2×#41×C67 | C22 | semidirect |
| 36. C22×D4×C67 | C22 | semidirect |
| 62. #41×C67 | D4 | semidirect |
| 76. C2×D4×C67 | D4 | semidirect |
| 152. C67 | #3008 | semidirect |
| 153. C2×H(5,𝔽2) | D67 | semidirect |
| 167. C2×#41 | C2×D67 | semidirect |
| 172. C22×D4 | C2×D67 | semidirect |
| 198. #41 | C22⋊D67 | semidirect |
| 217. C2×D4 | C22⋊D67 | semidirect |