Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14558255 | C2 | semidirect |
| 2. #14557926 | C2 | semidirect |
| 4. #14557755 | C2 | semidirect |
| 6. #14557742 | C2 | semidirect |
| 7. #14557663 | C2 | semidirect |
| 8. #14557632 | C2 | semidirect |
| 9. C4×Q16×C37 | C2 | semidirect |
| 111. C4×Q16 | D37 | semidirect |
| 112. C37 | #3402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558255 | 2 |
| #14557926 | 2 |
| #14557917 | 2 |
| #14557755 | 2 |
| #14557751 | 2 |
| #14557742 | 2 |
| #14557663 | 2 |
| #14557632 | 2 |
| C4×Q16×C37 | 2 |
| #3402 | 37 |