Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #14557941 | C2 | semidirect |
| 3. #14557939 | C2 | semidirect |
| 4. #14557937 | C2 | semidirect |
| 5. #14557935 | C2 | semidirect |
| 6. #14557934 | C2 | semidirect |
| 11. C37×#500 | C2 | semidirect |
| 66. #10596929 | Q8 | semidirect |
| 67. C8×D37 | Q8 | semidirect |
| 112. #500 | D37 | semidirect |
| 119. C37 | #3164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558160 | 2 |
| #14557941 | 2 |
| #14557939 | 2 |
| #14557937 | 2 |
| #14557935 | 2 |
| #14557934 | 2 |
| #14557574 | 2 |
| #14557570 | 2 |
| #107×D37 | 2 |
| #14557487 | 2 |
| C37×#500 | 2 |
| #3164 | 37 |