Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
At least 6865 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has at least 6865 conjugacy classes of subgroups — too many to draw. Only its 122 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. #72233208 | C2 | direct (N × H) |
| 3. C2×#11715843 | C2 | semidirect |
| 4. #11715843 | C22 | semidirect |
| 6. C2×#85645 | C4 | semidirect |
| 9. C2×C22⋊(C22⋊A4) | C2×C4 | semidirect |
| 11. #85645 | C2×C4 | semidirect |
| 13. C23×#120 | Dic3 | semidirect |
| 15. C22⋊(C22⋊A4) | C22×C4 | semidirect |
| 16. C27 | C2×Dic3 | semidirect |
| 19. C22×#120 | C2×Dic3 | semidirect |
| 21. C26 | SL(2,ℤ/4) | semidirect |
| 22. C26 | C22×Dic3 | semidirect |
| 26. C2×#120 | SL(2,ℤ/4) | semidirect |
| 29. C25 | C2×SL(2,ℤ/4) | semidirect |
| 30. C25 | C2×SL(2,ℤ/4) | semidirect |
| 34. #120 | C2×SL(2,ℤ/4) | semidirect |
| 37. C24 | C22×SL(2,ℤ/4) | semidirect |
| 38. C24 | #5936 | semidirect |
| 41. C23 | #73080 | semidirect |
| 44. C23 | C2×#5936 | semidirect |
| 46. C22 | C2×#73080 | semidirect |
| 50. C2 | #72233208 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#359501 | 3 |
| #72233208 | 2 |
| C22×#85645 | 2 |
| C2×#11715843 | 2 |
| C22×#5936 | 4 |
| C2×#73080 | 4 |