Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
504 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 193 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×C37 | C23 |
| hypercenter | #380 | D37 |
| hypocenter | C37 | #2347 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14557429 | C2 | semidirect |
| 4. #14557400 | C2 | semidirect |
| 5. C4⋊C4×Dic37 | C2 | semidirect |
| 6. #14557384 | C2 | semidirect |
| 9. #11924495 | C4 | semidirect |
| 103. C37 | #2347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924495 | 2 |
| #14557429 | 2 |
| #14557421 | 2 |
| #14557400 | 2 |
| C4⋊C4×Dic37 | 2 |
| #14557384 | 2 |
| C4×C22⋊Dic37 | 2 |
| C37×#380 | 2 |
| #2347 | 37 |