Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 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×#381 | C2 |
| socle, cosocle | C23×C37 | C24 |
| prime radical | C23×D148 | C2 |
| hypercenter | #381 | D37 |
| hypocenter | C37 | #2308 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C4×D37 | C2 | semidirect |
| 3. #14557411 | C2 | semidirect |
| 4. #14557396 | C2 | semidirect |
| 5. #14557388 | C2 | semidirect |
| 6. C37×#381 | C2 | semidirect |
| 10. C22×D148 | C4 | semidirect |
| 12. C22×C4×D37 | C22 | semidirect |
| 14. C2×#10596938 | C22 | semidirect |
| 15. C2×#10596938 | C22 | semidirect |
| 17. #11924443 | C22 | semidirect |
| 20. #95×C37 | C22 | semidirect |
| 26. C23×D37 | C2×C4 | semidirect |
| 31. C22×C4×C37 | C2×C4 | semidirect |
| 38. C2×D148 | C2×C4 | semidirect |
| 57. C22×D37 | C22⋊C4 | semidirect |
| 100. #381 | D37 | semidirect |
| 102. C37 | #2308 | semidirect |
| 116. #95 | C2×D37 | semidirect |
| 134. C22×C4 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D148 | 2 |
| C2×C22⋊C4×D37 | 2 |
| #14557411 | 2 |
| #14557396 | 2 |
| #14557388 | 2 |
| C37×#381 | 2 |
| #2308 | 37 |