Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14558350 | C2 | semidirect |
| 2. #14558349 | C2 | semidirect |
| 3. #14558346 | C2 | semidirect |
| 4. #14557911 | C2 | semidirect |
| 5. #14557809 | C2 | semidirect |
| 6. #14557807 | C2 | semidirect |
| 7. #14557718 | C2 | semidirect |
| 8. #14557714 | C2 | semidirect |
| 9. #14557649 | C2 | semidirect |
| 10. #14557648 | C2 | semidirect |
| 11. C37×#473 | C2 | semidirect |
| 153. #473 | D37 | semidirect |
| 158. C37 | #3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558350 | 2 |
| #14558349 | 2 |
| #14558346 | 2 |
| #14557911 | 2 |
| #14557809 | 2 |
| #14557807 | 2 |
| #14557718 | 2 |
| #14557714 | 2 |
| #14557649 | 2 |
| #14557648 | 2 |
| C37×#473 | 2 |
| #3293 | 37 |