Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
360 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#3866 |
| commutator, socle | C2×C37 | C23×C8 |
| Fitting | #131×C37 | C4 |
| prime radical | #41×D37 | C4 |
| cosocle | #64436 | C24 |
| hypercenter | #131 | #3866 |
| hypocenter | C37 | #3407 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C4 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14558592 | C2 | semidirect |
| 2. #14558591 | C2 | semidirect |
| 3. C2×#11924611 | C2 | semidirect |
| 4. D37⋊M32 | C2 | semidirect |
| 8. #11924611 | C22 | semidirect |
| 9. #11924610 | C22 | semidirect |
| 10. D37⋊C16 | C22 | semidirect |
| 11. C2×#10596927 | C22 | semidirect |
| 71. C37 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558592 | 2 |
| #14558591 | 2 |
| C2×#11924611 | 2 |
| D37⋊M32 | 2 |
| #131×D37 | 2 |
| #3407 | 37 |