Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
608 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 170 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×D4×#3866 | C2 | semidirect |
| 2. #14558574 | C2 | direct (N × H) |
| 3. C2×#11924604 | C2 | semidirect |
| 4. C2×#11924598 | C2 | semidirect |
| 5. C2×#11924590 | C2 | semidirect |
| 10. D4×#3866 | C22 | semidirect |
| 14. #11924604 | C22 | semidirect |
| 15. #11924598 | C22 | semidirect |
| 16. #11924590 | C22 | semidirect |
| 18. C2×D296 | C4 | semidirect |
| 19. C2×#10596939 | C4 | semidirect |
| 20. D8×D37 | C4 | semidirect |
| 23. C2×D8×C37 | C4 | semidirect |
| 29. C2×D4×C37 | C2×C4 | semidirect |
| 33. D4×D37 | C2×C4 | semidirect |
| 35. C2×D148 | C2×C4 | semidirect |
| 45. D8×C37 | C2×C4 | semidirect |
| 46. C2×C8×C37 | C2×C4 | semidirect |
| 47. #10596939 | C2×C4 | semidirect |
| 48. C2×#64436 | C2×C4 | semidirect |
| 49. D296 | C2×C4 | semidirect |
| 50. C8×D37 | C2×C4 | semidirect |
| 65. D4×C37 | C22×C4 | semidirect |
| 71. D148 | C22×C4 | semidirect |
| 77. C8×C37 | C22×C4 | semidirect |
| 78. #64436 | C22×C4 | semidirect |
| 98. C2×C37 | #442 | semidirect |
| 101. D37 | #442 | semidirect |
| 109. C37 | C2×#442 | semidirect |
| 116. C2×D8 | #3866 | semidirect |
| 134. C2×D4 | C2×#3866 | semidirect |
| 142. D8 | C2×#3866 | semidirect |
| 149. C2×C8 | C2×#3866 | semidirect |
| 167. D4 | C22×#3866 | semidirect |
| 181. C8 | C22×#3866 | semidirect |
| 203. C2 | #14558574 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#3866 | 2 |
| #14558574 | 2 |
| C2×#11924604 | 2 |
| C2×#11924598 | 2 |
| C2×#11924590 | 2 |
| C2×D8×D37 | 2 |
| C2×#442 | 37 |