Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#14524023 | C2 | semidirect |
| 3. #16863740 | C2 | semidirect |
| 4. #16863731 | C2 | semidirect |
| 5. #16863655 | C2 | semidirect |
| 6. #16863641 | C2 | semidirect |
| 7. #16863559 | C2 | semidirect |
| 8. #16863554 | C2 | semidirect |
| 9. #16863534 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #481×C67 | C2 | semidirect |
| 15. C2×Dic268 | C22 | semidirect |
| 16. C2×#11761616 | C22 | semidirect |
| 32. #14523976 | C22 | semidirect |
| 33. #14523968 | C22 | semidirect |
| 34. #14523966 | C22 | semidirect |
| 35. #14523966 | C22 | semidirect |
| 40. #106×C67 | C22 | semidirect |
| 41. #102×C67 | C22 | semidirect |
| 150. C67 | #3196 | semidirect |
| 155. #481 | D67 | semidirect |
| 185. #106 | C2×D67 | semidirect |
| 189. #102 | C2×D67 | semidirect |