Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 10. #11924591 | C4 | semidirect |
| 11. #11924590 | C4 | semidirect |
| 12. C8×#3866 | C4 | semidirect |
| 15. #11924447 | C4 | semidirect |
| 16. #11924446 | C4 | semidirect |
| 17. #97×C37 | C4 | semidirect |
| 47. #64438 | C42 | semidirect |
| 48. C8×C37 | C42 | semidirect |
| 49. #64436 | C42 | semidirect |
| 55. #3866 | #97 | direct (N × H) |
| 70. C37 | C4×#97 | semidirect |
| 81. #97 | #3866 | direct (N × H) |
| 114. C8 | C4×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558492 | 2 |
| C2×#11924590 | 2 |
| C2×C8×#3866 | 2 |
| C42×#3866 | 2 |
| #97×D37 | 2 |
| C4×#97 | 37 |