Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1296 conjugacy classes of subgroups; only the 517 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 517 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D37 |
| commutator, socle, cosocle | C22×C37 | C25 |
| Fitting | C37×#543 | C2 |
| prime radical | C24×D37 | C22 |
| hypercenter | #543 | D37 |
| hypocenter | C37 | C2×#543 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #543 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14558159 | C2 | semidirect |
| 2. #14558158 | C2 | semidirect |
| 3. C22⋊Q8×D37 | C2 | semidirect |
| 5. C37×#543 | C2 | semidirect |
| 7. C2×Q8×D37 | C22 | semidirect |
| 9. #11924516 | C22 | semidirect |
| 10. #11924515 | C22 | semidirect |
| 11. #11924514 | C22 | semidirect |
| 12. #11924513 | C22 | semidirect |
| 13. #11924512 | C22 | semidirect |
| 14. C4⋊C4×D37 | C22 | semidirect |
| 19. C22⋊Q8×C37 | C22 | semidirect |
| 23. C23×D37 | Q8 | semidirect |
| 26. C2×Q8×C37 | C23 | semidirect |
| 33. C2×Dic74 | C23 | semidirect |
| 34. C4⋊C4×C37 | C23 | semidirect |
| 38. C4⋊Dic37 | C23 | semidirect |
| 39. #10596936 | C23 | semidirect |
| 41. C23×C37 | C2×Q8 | semidirect |
| 47. C22×D37 | C2×Q8 | semidirect |
| 75. D37 | #543 | direct (N × H) |
| 78. #543 | D37 | direct (N × H) |
| 81. C37 | C2×#543 | semidirect |
| 90. C22⋊Q8 | C2×D37 | semidirect |
| 104. C2×Q8 | C22×D37 | semidirect |
| 112. C4⋊C4 | C22×D37 | semidirect |
| 124. C23 | Q8×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558159 | 2 |
| #14558158 | 2 |
| C22⋊Q8×D37 | 2 |
| C2×C22⋊C4×D37 | 2 |
| C37×#543 | 2 |
| C2×#543 | 37 |