Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14558253 | C2 | semidirect |
| 3. #14557884 | C2 | semidirect |
| 4. #14557875 | C2 | semidirect |
| 5. #14557814 | C2 | semidirect |
| 6. #14557774 | C2 | semidirect |
| 7. #14557744 | C2 | semidirect |
| 8. #14557697 | C2 | semidirect |
| 9. C4×#10596930 | C2 | semidirect |
| 10. #14557530 | C2 | semidirect |
| 11. C8×D4×C37 | C2 | semidirect |
| 135. C8×D4 | D37 | semidirect |
| 137. C37 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558253 | 2 |
| #14558188 | 2 |
| #14557884 | 2 |
| #14557875 | 2 |
| #14557814 | 2 |
| #14557774 | 2 |
| #14557744 | 2 |
| #14557697 | 2 |
| C4×#10596930 | 2 |
| #14557530 | 2 |
| C8×D4×C37 | 2 |
| #3302 | 37 |