Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
462 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14524023 | C2 | semidirect |
| 3. #16863733 | C2 | semidirect |
| 4. #16863709 | C2 | semidirect |
| 5. #16863643 | C2 | semidirect |
| 6. #16863641 | C2 | semidirect |
| 7. #16863548 | C2 | semidirect |
| 8. #16863537 | C2 | semidirect |
| 9. #16863534 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #480×C67 | C2 | semidirect |
| 12. C22×Dic134 | C22 | semidirect |
| 16. C2×#11761617 | C22 | semidirect |
| 17. C2×#11761616 | C22 | semidirect |
| 18. C2×#11761611 | C22 | semidirect |
| 22. #14524023 | C22 | semidirect |
| 32. #14523976 | C22 | semidirect |
| 33. #14523968 | C22 | semidirect |
| 34. #14523966 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 36. C22⋊(C67⋊C8) | C22 | semidirect |
| 39. C2×C4⋊C4×C67 | C22 | semidirect |
| 40. #107×C67 | C22 | semidirect |
| 41. #102×C67 | C22 | semidirect |
| 42. C22⋊C8×C67 | C22 | semidirect |
| 160. C67 | #3193 | semidirect |
| 165. #480 | D67 | semidirect |
| 191. C2×C4⋊C4 | C2×D67 | semidirect |
| 195. #107 | C2×D67 | semidirect |
| 199. #102 | C2×D67 | semidirect |
| 202. C22⋊C8 | C2×D67 | semidirect |