Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 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 | C2×C37 | C24×C4 |
| Fitting | C37×#519 | C2 |
| socle, cosocle | C22×C37 | C25 |
| prime radical | C23×D37 | C23 |
| hypercenter | #519 | D37 |
| hypocenter | C37 | C2×#519 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14558011 | C2 | semidirect |
| 3. #14558010 | C2 | semidirect |
| 4. #14558009 | C2 | semidirect |
| 5. C4×Q8×D37 | C2 | semidirect |
| 7. C37×#519 | C2 | semidirect |
| 9. C2×Q8×D37 | C4 | semidirect |
| 13. Q8×Dic37 | C22 | semidirect |
| 14. C4×Dic74 | C22 | semidirect |
| 15. #11924501 | C22 | semidirect |
| 24. C4×Q8×C37 | C22 | semidirect |
| 27. C2×Q8×C37 | C2×C4 | semidirect |
| 32. Q8×D37 | C2×C4 | semidirect |
| 37. C2×Dic74 | C2×C4 | semidirect |
| 81. D37 | #519 | direct (N × H) |
| 86. #519 | D37 | direct (N × H) |
| 89. C37 | C2×#519 | semidirect |
| 99. C4×Q8 | C2×D37 | semidirect |
| 113. C2×Q8 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D37 | 2 |
| #14558011 | 2 |
| #14558010 | 2 |
| #14558009 | 2 |
| C4×Q8×D37 | 2 |
| #117×D37 | 2 |
| C37×#519 | 2 |
| C2×#519 | 37 |