Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
156 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 64 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. #14558460 | C2 | semidirect |
| 4. #14558459 | C2 | semidirect |
| 14. #11924476 | C4 | semidirect |
| 15. #11924475 | C4 | semidirect |
| 17. M32×C37 | C4 | semidirect |
| 32. C16×C37 | C2×C4 | semidirect |
| 33. #10596925 | C2×C4 | semidirect |
| 72. C37 | #2159 | semidirect |
| 78. M32 | #3866 | semidirect |
| 100. C16 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558543 | 2 |
| C2×#11924605 | 2 |
| #14558460 | 2 |
| #14558459 | 2 |
| M32×D37 | 2 |
| #2159 | 37 |