Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #14558088 | C2 | semidirect |
| 3. #14557839 | C2 | semidirect |
| 4. #14557831 | C2 | semidirect |
| 5. #14557829 | C2 | semidirect |
| 6. #14557823 | C2 | semidirect |
| 7. #14557815 | C2 | semidirect |
| 8. #14557570 | C2 | semidirect |
| 9. C4⋊C8×D37 | C2 | semidirect |
| 11. C37×#474 | C2 | semidirect |
| 50. #10596964 | Q8 | semidirect |
| 142. #474 | D37 | semidirect |
| 146. C37 | #3076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558088 | 2 |
| C4×#10596964 | 2 |
| #14557839 | 2 |
| #14557831 | 2 |
| #14557829 | 2 |
| #14557823 | 2 |
| #14557815 | 2 |
| #14557570 | 2 |
| C4⋊C8×D37 | 2 |
| #14557526 | 2 |
| C37×#474 | 2 |
| #3076 | 37 |