Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 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. C2×M16×D67 | C2 | semidirect |
| 3. C2×#14524019 | C2 | semidirect |
| 4. #16863651 | C2 | semidirect |
| 5. #16863639 | C2 | semidirect |
| 6. #16863634 | C2 | semidirect |
| 7. #16863622 | C2 | semidirect |
| 8. #16863438 | C2 | semidirect |
| 9. #16863405 | C2 | semidirect |
| 10. #16863397 | C2 | semidirect |
| 11. C2×#137×C67 | C2 | semidirect |
| 33. #14523977 | C22 | semidirect |
| 34. #14523975 | C22 | semidirect |
| 35. #14523967 | C22 | semidirect |
| 36. #14523967 | C22 | semidirect |
| 37. #14523967 | C22 | semidirect |
| 38. #14523964 | C22 | semidirect |
| 42. C2×Q16×C67 | C22 | semidirect |
| 43. C2×SD16×C67 | C22 | semidirect |
| 90. M16×C67 | D4 | semidirect |
| 145. C2×D67 | #137 | semidirect |
| 164. C67 | #3056 | semidirect |
| 165. C2×#137 | D67 | semidirect |
| 180. C2×Q16 | C2×D67 | semidirect |
| 181. C2×SD16 | C2×D67 | semidirect |
| 236. M16 | C22⋊D67 | semidirect |