Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
760 conjugacy classes of subgroups; only the 434 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 434 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #3866 |
| commutator, hypocenter | C37 | C22×C4×C8 |
| Frattini | C22 | C23×#3866 |
| Fitting | C2×C42×C37 | C4 |
| socle | C23×C37 | C22×C4 |
| prime radical | C23×D37 | C2×C4 |
| cosocle | C2×Dic37 | C24 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×D37⋊C8 | C2 | direct (N × H) |
| 3. C2×C4×#64438 | C2 | semidirect |
| 5. C2×D37⋊C8 | C4 | direct (N × H) |
| 8. C4×#64438 | C22 | semidirect |
| 21. C2×C4×D37 | C8 | semidirect |
| 26. C2×#64438 | C2×C4 | semidirect |
| 28. D37⋊C8 | C2×C4 | direct (N × H) |
| 38. C2×C4×C37 | C2×C8 | semidirect |
| 41. C2×Dic37 | C2×C8 | semidirect |
| 47. C4×D37 | C2×C8 | semidirect |
| 49. #64438 | C22×C4 | semidirect |
| 53. C2×D37 | C4×C8 | semidirect |
| 57. C4×C37 | C22×C8 | semidirect |
| 59. Dic37 | C22×C8 | semidirect |
| 62. C2×C37 | C2×C4×C8 | semidirect |
| 65. D37 | C2×C4×C8 | semidirect |
| 70. C37 | C22×C4×C8 | semidirect |
| 111. C2×C4 | D37⋊C8 | direct (N × H) |
| 126. C4 | C2×D37⋊C8 | direct (N × H) |
| 128. C2 | C4×D37⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D37⋊C8 | 2 |
| C4×D37⋊C8 | 2 |
| C2×C4×#64438 | 2 |
| C2×C42×D37 | 2 |
| C22×C4×C8 | 37 |