Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
428 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 217 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 | C2×#125×C37 | C2 |
| socle, prime radical, cosocle | C23×C37 | C24 |
| hypercenter | C2×#125 | D37 |
| hypocenter | C37 | #2336 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 26. #125×C37 | C4 | semidirect |
| 108. C37 | #2336 | semidirect |
| 109. #125 | Dic37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557432 | 2 |
| #14557419 | 2 |
| #14557401 | 2 |
| C4⋊C4×Dic37 | 2 |
| C4×C4⋊Dic37 | 2 |
| C2×#125×C37 | 2 |
| #2336 | 37 |