Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
At least 6484 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has at least 6484 conjugacy classes of subgroups — too many to draw. Only its 200 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×#14694⋊C3 | C2 | semidirect |
| 2. C2×#11715572 | C2 | semidirect |
| 3. C2×#11711331 | C2 | semidirect |
| 4. C22×#72991 | C2 | semidirect |
| 5. C22×C4⋊#1020 | C2 | semidirect |
| 6. C22×#73081 | C2 | semidirect |
| 7. C23×#1020⋊C2 | C2 | semidirect |
| 8. #72220509 | C2 | direct (N × H) |
| 11. C23×#1020 | C22 | semidirect |
| 12. C2×C4⋊#1020 | C22 | semidirect |
| 13. C22×#5936 | C22 | semidirect |
| 14. #11715572 | C22 | semidirect |
| 15. C22×#1020⋊C2 | C22 | semidirect |
| 16. C2×#72991 | C22 | semidirect |
| 17. C2×#73081 | C22 | semidirect |
| 18. #11711331 | C22 | semidirect |
| 19. C22×C4×C22⋊A4 | C22 | semidirect |
| 21. C22×#379⋊C3 | C22 | semidirect |
| 22. #14694⋊C3 | C22 | semidirect |
| 23. C2×#14694 | D3 | semidirect |
| 25. C22×#1020 | D4 | semidirect |
| 26. C22×#1020 | D4 | semidirect |
| 29. C22×#1020 | C23 | semidirect |
| 30. C2×C4×C22⋊A4 | C23 | semidirect |
| 31. C2×#5936 | C23 | semidirect |
| 32. C22×#120⋊C3 | D4 | semidirect |
| 34. C2×#379⋊C3 | C23 | semidirect |
| 35. C26×C4 | C2×D3 | semidirect |
| 37. C22×#379 | C2×D3 | semidirect |
| 38. #14694 | C2×D3 | semidirect |
| 43. C2×#1020 | C2×D4 | semidirect |
| 44. C2×#1020 | C2×D4 | semidirect |
| 45. C2×#120⋊C3 | C2×D4 | semidirect |
| 47. C25×C4 | C22×D3 | semidirect |
| 48. C22×#120 | D12 | semidirect |
| 50. C23×C22⋊C4 | S4 | semidirect |
| 51. C2×#379 | C22×D3 | semidirect |
| 52. C2×C22⋊A4 | #120 | semidirect |
| 63. C2×#120 | C2×D12 | semidirect |
| 64. C22×C22⋊C4 | C2×S4 | semidirect |
| 65. C22⋊A4 | C2×#120 | semidirect |
| 66. C25 | #882 | semidirect |
| 67. C25 | C4⋊S4 | semidirect |
| 75. C24 | C2×#882 | semidirect |
| 77. C24 | C2×C4⋊S4 | semidirect |
| 81. C22×C4 | #1020⋊C2 | semidirect |
| 87. C2×C4 | C2×#1020⋊C2 | semidirect |
| 94. C2 | #72220509 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14694⋊C3 | 2 |
| C2×#11715572 | 2 |
| C2×#11711331 | 2 |
| C2×#417526 | 3 |
| C22×#72991 | 2 |
| C22×C4⋊#1020 | 2 |
| C22×#73081 | 2 |
| C23×#1020⋊C2 | 2 |
| #72220509 | 2 |
| C2×#85297 | 4 |