Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
At least 6549 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has at least 6549 conjugacy classes of subgroups — too many to draw. Only its 94 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. #72247700 | C2 | semidirect |
| 2. #72247638 | C2 | semidirect |
| 3. #72247524 | C2 | semidirect |
| 4. #72227646 | C2 | semidirect |
| 5. C4×#87520 | C2 | semidirect |
| 7. #72215648 | C2 | semidirect |
| 8. #11715831 | C4 | semidirect |
| 9. #11715830 | C4 | semidirect |
| 10. #11715829 | C4 | semidirect |
| 11. #11715828 | C4 | semidirect |
| 14. #11715667 | C22 | semidirect |
| 15. #11715663 | C22 | semidirect |
| 17. #11710873 | C22 | semidirect |
| 18. C4×#5950 | C22 | semidirect |
| 19. #10574065 | D3 | semidirect |
| 20. #87548 | C2×C4 | semidirect |
| 21. #87547 | C2×C4 | semidirect |
| 23. #87522 | C2×C4 | semidirect |
| 28. #87518 | C2×C4 | semidirect |
| 32. #63076 | C2×D3 | semidirect |
| 33. C4×#585 | C2×D3 | semidirect |
| 37. #5935 | C22⋊C4 | semidirect |
| 38. #5935 | C22⋊C4 | semidirect |
| 39. #5933 | C22⋊C4 | semidirect |
| 40. #5933 | C22⋊C4 | semidirect |
| 41. 2−1+6 | C4×D3 | semidirect |
| 42. H(7,𝔽2) | C4×D3 | semidirect |
| 44. #2901 | S4 | semidirect |
| 52. #568 | C2×S4 | semidirect |
| 54. C4×#41 | C2×S4 | semidirect |
| 56. 2−1+4 | C4×S4 | semidirect |
| 58. H(5,𝔽2) | C4×S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72247700 | 2 |
| #72247638 | 2 |
| #72247524 | 2 |
| #72241172 | 3 |
| #72227646 | 2 |
| C4×#87520 | 2 |
| #72215767 | 2 |
| #72215648 | 2 |
| #11712954 | 4 |
| S4×#104 | 4 |