Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 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. #14558346 | C2 | semidirect |
| 2. #14557975 | C2 | semidirect |
| 3. #14557974 | C2 | semidirect |
| 4. #14557966 | C2 | semidirect |
| 5. #14557965 | C2 | semidirect |
| 6. Q32×D37 | C2 | semidirect |
| 7. #14557949 | C2 | semidirect |
| 8. C2×Q32×C37 | C2 | semidirect |
| 88. C2×Q32 | D37 | semidirect |
| 90. C37 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558346 | 2 |
| #14557975 | 2 |
| #14557974 | 2 |
| #14557966 | 2 |
| #14557965 | 2 |
| Q32×D37 | 2 |
| #14557949 | 2 |
| C2×Q32×C37 | 2 |
| #3417 | 37 |