Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #14557581 | C2 | semidirect |
| 5. #14557305 | C2 | semidirect |
| 6. #14557293 | C2 | semidirect |
| 7. C4×M16×C37 | C2 | semidirect |
| 16. #11924454 | C4 | semidirect |
| 17. #11924452 | C4 | semidirect |
| 100. C4×M16 | D37 | semidirect |
| 103. C37 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557581 | 2 |
| #14557549 | 2 |
| C2×#11924464 | 2 |
| #14557515 | 2 |
| #14557305 | 2 |
| #14557293 | 2 |
| C4×M16×C37 | 2 |
| #1932 | 37 |