Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
484 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#3866 |
| commutator, socle | C22×C37 | C23×C4 |
| Fitting | #125×C37 | C4 |
| prime radical, cosocle | C22×D37 | C24 |
| hypercenter | #125 | #3866 |
| hypocenter | C37 | C4×#125 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. #11924528 | C4 | semidirect |
| 19. #11924527 | C4 | semidirect |
| 20. #11924526 | C4 | semidirect |
| 24. #125×C37 | C4 | semidirect |
| 80. #3866 | #125 | direct (N × H) |
| 100. C37 | C4×#125 | semidirect |
| 104. #125 | #3866 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558484 | 2 |
| #14558482 | 2 |
| #14558477 | 2 |
| C4⋊C4×#3866 | 2 |
| C42×#3866 | 2 |
| #125×D37 | 2 |
| C4×#125 | 37 |