Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 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×D283 |
| commutator, socle, cosocle | C22×C283 | C25 |
| Fitting | H(3,𝔽4)×C283 | C2 |
| hypercenter | H(3,𝔽4) | D283 |
| hypocenter | C283 | #3529 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31827215 | C2 | semidirect |
| 2. #31827209 | C2 | semidirect |
| 3. #31827204 | C2 | semidirect |
| 4. #31827014 | C2 | semidirect |
| 5. #31826994 | C2 | semidirect |
| 6. #31826971 | C2 | semidirect |
| 7. H(3,𝔽4)×C283 | C2 | semidirect |
| 8. C2×#17985393 | C22 | semidirect |
| 10. C23×Dic283 | C22 | semidirect |
| 11. #22583608 | C22 | semidirect |
| 13. #22583603 | C22 | semidirect |
| 14. #22583602 | C22 | semidirect |
| 15. #22583598 | C22 | semidirect |
| 16. #22583594 | C22 | semidirect |
| 17. #22583592 | C22 | semidirect |
| 19. #22583587 | C22 | semidirect |
| 20. #22583586 | C22 | semidirect |
| 21. #22583583 | C22 | semidirect |
| 24. #22583579 | C22 | semidirect |
| 25. Q8×Dic283 | C22 | semidirect |
| 27. (C22⋊D283)⋊C4 | C22 | semidirect |
| 28. #22583566 | C22 | semidirect |
| 29. C42×D283 | C22 | semidirect |
| 97. C283 | #3529 | semidirect |
| 101. H(3,𝔽4) | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827215 | 2 |
| #31827209 | 2 |
| #31827204 | 2 |
| #31827014 | 2 |
| #31826994 | 2 |
| #31826971 | 2 |
| H(3,𝔽4)×C283 | 2 |
| #3529 | 283 |