Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
492 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 2. #14558544 | C2 | semidirect |
| 3. #14558543 | C2 | semidirect |
| 12. #11924605 | C22 | semidirect |
| 13. #11924604 | C22 | semidirect |
| 15. C2×#10596934 | C4 | semidirect |
| 16. C2×#10596929 | C4 | semidirect |
| 17. M16×D37 | C4 | semidirect |
| 20. C2×M16×C37 | C4 | semidirect |
| 39. M16×C37 | C2×C4 | semidirect |
| 40. C2×C8×C37 | C2×C4 | semidirect |
| 41. #10596934 | C2×C4 | semidirect |
| 42. C2×#64436 | C2×C4 | semidirect |
| 43. #10596929 | C2×C4 | semidirect |
| 44. C8×D37 | C2×C4 | semidirect |
| 102. C37 | #2911 | semidirect |
| 108. C2×M16 | #3866 | semidirect |
| 133. M16 | C2×#3866 | semidirect |
| 137. C2×C8 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924615 | 2 |
| #14558544 | 2 |
| #14558543 | 2 |
| C2×M16×D37 | 2 |
| #2911 | 37 |