Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1212 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D37 |
| commutator, socle, cosocle | C22×C37 | C25 |
| Frattini | C22 | C24×D37 |
| Fitting | C22×C42×C37 | C2 |
| hypercenter | C22×C42 | D37 |
| hypocenter | C37 | #3444 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14558090 | C2 | semidirect |
| 2. #14558083 | C2 | semidirect |
| 3. #14558067 | C2 | semidirect |
| 4. #14558044 | C2 | semidirect |
| 5. C4×#10596962 | C2 | semidirect |
| 6. C22×C42×C37 | C2 | semidirect |
| 8. #11924536 | C22 | semidirect |
| 9. #11924533 | C22 | semidirect |
| 10. #11924530 | C22 | semidirect |
| 11. #11924528 | C22 | semidirect |
| 12. #11924524 | C22 | semidirect |
| 17. C4×Dic74 | C22 | semidirect |
| 18. C4×D148 | C22 | semidirect |
| 21. #11924493 | C22 | semidirect |
| 22. C42×D37 | C22 | semidirect |
| 55. C2×C4×C37 | #41 | semidirect |
| 82. C22×C42 | D37 | semidirect |
| 83. C37 | #3444 | semidirect |
| 137. C2×C4 | #10596962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558090 | 2 |
| #14558083 | 2 |
| #14558067 | 2 |
| #14558044 | 2 |
| C4×#10596962 | 2 |
| C22×C42×C37 | 2 |
| #3444 | 37 |