Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D67 | C2 | semidirect |
| 2. C2×#14524072 | C2 | semidirect |
| 4. #16863554 | C2 | semidirect |
| 5. #16863553 | C2 | semidirect |
| 6. #16863552 | C2 | semidirect |
| 7. #16863534 | C2 | semidirect |
| 8. #16863533 | C2 | semidirect |
| 9. #16863403 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #448×C67 | C2 | semidirect |
| 23. C2×Dic268 | C22 | semidirect |
| 24. C2×#11761618 | C22 | semidirect |
| 25. C2×#11761616 | C22 | semidirect |
| 35. #14523968 | C22 | semidirect |
| 36. #14523967 | C22 | semidirect |
| 37. #14523966 | C22 | semidirect |
| 41. C2×SD16×C67 | C22 | semidirect |
| 43. #103×C67 | C22 | semidirect |
| 59. Q8×D67 | D4 | semidirect |
| 144. C22×C67 | #137 | semidirect |
| 152. C2×D67 | #137 | semidirect |
| 170. C67 | #3004 | semidirect |
| 179. #448 | D67 | semidirect |
| 197. C2×SD16 | C2×D67 | semidirect |
| 211. #103 | C2×D67 | semidirect |
| 321. C22 | #14524072 | semidirect |