Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D37 |
| commutator | C22×C37 | C23×C4 |
| Fitting | C37×#380 | C2 |
| socle, cosocle | C23×C37 | C24 |
| prime radical | C24×D37 | C22 |
| hypercenter | #380 | D37 |
| hypocenter | C37 | #2315 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14557407 | C2 | semidirect |
| 4. #14557404 | C2 | semidirect |
| 5. #14557393 | C2 | semidirect |
| 6. #14557391 | C2 | semidirect |
| 7. C37×#380 | C2 | semidirect |
| 11. C2×C4⋊Dic37 | C22 | semidirect |
| 12. C2×#10596936 | C22 | semidirect |
| 14. C2×#10596938 | C4 | semidirect |
| 19. #11924443 | C22 | semidirect |
| 20. #11924443 | C22 | semidirect |
| 22. C2×C4⋊C4×C37 | C22 | semidirect |
| 24. #95×C37 | C22 | semidirect |
| 33. C22×C4×C37 | C2×C4 | semidirect |
| 38. C22×Dic37 | C2×C4 | semidirect |
| 48. #10596938 | C2×C4 | semidirect |
| 49. #10596938 | C2×C4 | semidirect |
| 64. C22×D37 | C4⋊C4 | semidirect |
| 118. #380 | D37 | semidirect |
| 119. C37 | #2315 | semidirect |
| 126. C2×C4⋊C4 | C2×D37 | semidirect |
| 136. #95 | C2×D37 | semidirect |
| 152. C22×C4 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596938 | 2 |
| C2×C22⋊C4×D37 | 2 |
| #14557407 | 2 |
| #14557404 | 2 |
| #14557393 | 2 |
| #14557391 | 2 |
| C37×#380 | 2 |
| #2315 | 37 |