Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
908 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 203 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, socle, cosocle | C23×C37 | C24 |
| Fitting | C37×#399 | C2 |
| prime radical | C24×D37 | C22 |
| hypercenter | #399 | D37 |
| hypocenter | C37 | C2×#399 |
| LCS | G ▷ C23×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊C4×D37 | C2 | semidirect |
| 3. #14557470 | C2 | semidirect |
| 4. #14557469 | C2 | semidirect |
| 5. #14557468 | C2 | semidirect |
| 6. #95×D37 | C2 | semidirect |
| 7. C37×#399 | C2 | semidirect |
| 11. C2×C4⋊Dic37 | C22 | semidirect |
| 12. C2×#10596936 | C22 | semidirect |
| 18. #11924443 | C22 | semidirect |
| 19. C2×C4⋊C4×C37 | C22 | semidirect |
| 21. #95×C37 | C22 | semidirect |
| 89. D37 | #399 | direct (N × H) |
| 95. #399 | D37 | direct (N × H) |
| 97. C37 | C2×#399 | semidirect |
| 104. C2×C4⋊C4 | C2×D37 | semidirect |
| 111. #95 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D37 | 2 |
| C2×C22⋊C4×D37 | 2 |
| #14557470 | 2 |
| #14557469 | 2 |
| #14557468 | 2 |
| #95×D37 | 2 |
| C37×#399 | 2 |
| C2×#399 | 37 |