Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1492 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 557 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 | C23×Q8×C37 | C2 |
| hypercenter | C23×Q8 | D37 |
| hypocenter | C37 | #3486 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11924584 | C2 | semidirect |
| 2. Q8×C22⋊D37 | C2 | semidirect |
| 3. #14558194 | C2 | semidirect |
| 4. #14558107 | C2 | semidirect |
| 5. #14558044 | C2 | semidirect |
| 6. #14558011 | C2 | semidirect |
| 7. C23×Q8×C37 | C2 | semidirect |
| 9. C2×#10596966 | C22 | semidirect |
| 11. C2×Q8×D37 | C22 | semidirect |
| 12. #11924534 | C22 | semidirect |
| 13. #11924525 | C22 | semidirect |
| 16. #11924512 | C22 | semidirect |
| 19. Q8×Dic37 | C22 | semidirect |
| 30. C2×Q8×C37 | D4 | semidirect |
| 75. C22×C37 | 2−1+4 | semidirect |
| 90. C23×Q8 | D37 | semidirect |
| 96. C37 | #3486 | semidirect |
| 123. C2×Q8 | C22⋊D37 | semidirect |
| 166. C22 | #11924584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924584 | 2 |
| Q8×C22⋊D37 | 2 |
| #14558194 | 2 |
| #14558107 | 2 |
| #14558044 | 2 |
| #14558011 | 2 |
| C23×Q8×C37 | 2 |
| #3486 | 37 |