Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
388 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C2×#11924590 | C2 | semidirect |
| 4. C4⋊C4×#3866 | C2 | semidirect |
| 5. #14558407 | C2 | semidirect |
| 6. #14558406 | C2 | semidirect |
| 11. D4×#3866 | C4 | semidirect |
| 17. #11924598 | C4 | semidirect |
| 23. #11924458 | C4 | semidirect |
| 24. #11924457 | C4 | semidirect |
| 25. #11924456 | C4 | semidirect |
| 26. #102×C37 | C4 | semidirect |
| 49. C4⋊#3866 | C2×C4 | semidirect |
| 54. D37⋊C8 | C2×C4 | semidirect |
| 55. C2×C8×C37 | C2×C4 | semidirect |
| 56. C4⋊C4×C37 | C2×C4 | semidirect |
| 57. C4⋊Dic37 | C2×C4 | semidirect |
| 59. C2×#64436 | C2×C4 | semidirect |
| 85. D4×C37 | C42 | semidirect |
| 93. D148 | C42 | semidirect |
| 147. C37 | #1762 | semidirect |
| 164. #102 | #3866 | semidirect |
| 190. C2×C8 | C2×#3866 | semidirect |
| 197. C4⋊C4 | C2×#3866 | semidirect |
| 216. D4 | C4×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#3866 | 2 |
| C2×#11924598 | 2 |
| C2×#11924590 | 2 |
| C4⋊C4×#3866 | 2 |
| #14558407 | 2 |
| #14558406 | 2 |
| #102×D37 | 2 |
| #1762 | 37 |