Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
196 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#3866 |
| commutator, socle | C2×C37 | C2×C4×C8 |
| Fitting | M32×C37 | C4 |
| prime radical | C22×D37 | C2×C8 |
| cosocle | C8×D37 | C23 |
| hypercenter | M32 | #3866 |
| hypocenter | C37 | C4×M32 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C8 ◁ M32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14558420 | C2 | semidirect |
| 4. C16×#3866 | C2 | semidirect |
| 8. #11924611 | C4 | semidirect |
| 9. #11924610 | C4 | semidirect |
| 16. #11924476 | C4 | semidirect |
| 17. #11924475 | C4 | semidirect |
| 19. M32×C37 | C4 | semidirect |
| 35. #10596927 | C2×C4 | semidirect |
| 36. C16×C37 | C2×C4 | semidirect |
| 37. #10596925 | C2×C4 | semidirect |
| 59. #3866 | M32 | direct (N × H) |
| 74. C37 | C4×M32 | semidirect |
| 82. M32 | #3866 | direct (N × H) |
| 106. C16 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D37⋊M32 | 2 |
| C2×C8×#3866 | 2 |
| #14558420 | 2 |
| C16×#3866 | 2 |
| M32×D37 | 2 |
| C4×M32 | 37 |