Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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. #14558600 | C2 | semidirect |
| 2. #14558574 | C2 | semidirect |
| 3. D8×#3866 | C2 | semidirect |
| 4. #14558543 | C2 | semidirect |
| 5. #14558525 | C2 | semidirect |
| 6. #14558496 | C2 | semidirect |
| 10. D4×#3866 | C22 | semidirect |
| 14. #11924605 | C22 | semidirect |
| 15. #11924604 | C22 | semidirect |
| 16. #11924598 | C22 | semidirect |
| 17. #11924590 | C22 | semidirect |
| 18. C8×#3866 | C22 | semidirect |
| 20. C2×D296 | C4 | semidirect |
| 21. C2×#10596939 | C4 | semidirect |
| 22. D8×D37 | C4 | semidirect |
| 23. D8×D37 | C4 | semidirect |
| 27. C2×D8×C37 | C4 | semidirect |
| 30. C2×D4×C37 | C2×C4 | semidirect |
| 34. D4×D37 | C2×C4 | semidirect |
| 36. C2×D148 | C2×C4 | semidirect |
| 48. D8×C37 | C2×C4 | semidirect |
| 49. D8×C37 | C2×C4 | semidirect |
| 50. C2×C8×C37 | C2×C4 | semidirect |
| 51. #10596939 | C2×C4 | semidirect |
| 52. #10596939 | C2×C4 | semidirect |
| 53. C2×#64436 | C2×C4 | semidirect |
| 54. D296 | C2×C4 | semidirect |
| 55. D296 | C2×C4 | semidirect |
| 56. C8×D37 | C2×C4 | semidirect |
| 57. C8×D37 | C2×C4 | semidirect |
| 116. C37 | #2948 | semidirect |
| 124. C2×D8 | #3866 | semidirect |
| 144. C2×D4 | C2×#3866 | semidirect |
| 151. D8 | C2×#3866 | semidirect |
| 152. D8 | C2×#3866 | semidirect |
| 161. C2×C8 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558600 | 2 |
| #14558574 | 2 |
| D8×#3866 | 2 |
| #14558543 | 2 |
| #14558525 | 2 |
| #14558496 | 2 |
| C2×D8×D37 | 2 |
| #2948 | 37 |