Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D37 |
| commutator, socle | C2×C37 | C23×C8 |
| Fitting | C37×#504 | C2 |
| prime radical | #41×D37 | C4 |
| cosocle | C8×C37 | C24 |
| hypercenter | #504 | D37 |
| hypocenter | C37 | #3407 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C8 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14557951 | C2 | semidirect |
| 3. #14557950 | C2 | semidirect |
| 4. #14557949 | C2 | semidirect |
| 5. C2×#11924475 | C2 | semidirect |
| 6. M32×D37 | C2 | semidirect |
| 7. C37×#504 | C2 | semidirect |
| 14. #11924476 | C22 | semidirect |
| 17. #11924475 | C22 | semidirect |
| 18. #11924475 | C22 | semidirect |
| 19. C2×#10596925 | C22 | semidirect |
| 20. C16×D37 | C22 | semidirect |
| 22. M32×C37 | C22 | semidirect |
| 23. C2×C16×C37 | C22 | semidirect |
| 77. #504 | D37 | semidirect |
| 80. C37 | #3407 | semidirect |
| 93. M32 | C2×D37 | semidirect |
| 96. C2×C16 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D37 | 2 |
| #14557951 | 2 |
| #14557950 | 2 |
| #14557949 | 2 |
| C2×#11924475 | 2 |
| M32×D37 | 2 |
| C37×#504 | 2 |
| #3407 | 37 |