Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D37 |
| commutator, cosocle | C22×C37 | C25 |
| Frattini | C22 | C24×D37 |
| Fitting | C2×C4⋊Q8×C37 | C2 |
| socle | C23×C37 | C24 |
| hypercenter | C2×C4⋊Q8 | D37 |
| hypocenter | C37 | C2×#555 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14558249 | C2 | direct (N × H) |
| 2. C2×#11924525 | C2 | semidirect |
| 3. C2×#11924511 | C2 | semidirect |
| 4. C2×C4×D148 | C2 | semidirect |
| 5. C2×#11924494 | C2 | semidirect |
| 6. C2×C4⋊Q8×C37 | C2 | semidirect |
| 10. #11924525 | C22 | semidirect |
| 11. #11924511 | C22 | semidirect |
| 12. C4×D148 | C22 | semidirect |
| 13. #11924494 | C22 | semidirect |
| 19. C4⋊Q8×C37 | C22 | semidirect |
| 70. C2×C37 | #555 | semidirect |
| 75. C2×C4⋊Q8 | D37 | semidirect |
| 80. C37 | C2×#555 | semidirect |
| 85. C4⋊Q8 | C2×D37 | semidirect |
| 144. C2 | #14558249 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558249 | 2 |
| C2×#11924525 | 2 |
| C2×#11924511 | 2 |
| C2×C4×D148 | 2 |
| C2×#11924494 | 2 |
| C2×C4⋊Q8×C37 | 2 |
| C2×#555 | 37 |