Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1258 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 455 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×D19 |
| commutator, socle, cosocle | C22×C19 | C25 |
| Fitting | C19×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D19 |
| hypocenter | C19 | #3549 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927286 | C2 | semidirect |
| 2. #11927256 | C2 | semidirect |
| 3. #11927176 | C2 | semidirect |
| 4. #11927112 | C2 | semidirect |
| 5. #11927109 | C2 | semidirect |
| 6. #11927093 | C2 | semidirect |
| 7. C19×H(3,𝔽4) | C2 | semidirect |
| 8. C22×C22⋊D19 | C22 | semidirect |
| 9. C2×#64545 | C22 | semidirect |
| 10. C2×#64543 | C22 | semidirect |
| 11. C2×D4×D19 | C22 | semidirect |
| 12. C19×#124 | C22 | semidirect |
| 13. C19×#124 | C22 | semidirect |
| 14. C19×#120 | C22 | semidirect |
| 15. #10597399 | C22 | semidirect |
| 16. #10597393 | C22 | semidirect |
| 17. #10597390 | C22 | semidirect |
| 19. #10597386 | C22 | semidirect |
| 20. #10597385 | C22 | semidirect |
| 21. #10597383 | C22 | semidirect |
| 22. #10597331 | C22 | semidirect |
| 23. #10597330 | C22 | semidirect |
| 24. #10597330 | C22 | semidirect |
| 25. #10597328 | C22 | semidirect |
| 26. #10597328 | C22 | semidirect |
| 27. (C22⋊D19)⋊C4 | C22 | semidirect |
| 28. #10597323 | C22 | semidirect |
| 29. #10597321 | C22 | semidirect |
| 30. #10597320 | C22 | semidirect |
| 31. #10597318 | C22 | semidirect |
| 32. C42×D19 | C22 | semidirect |
| 99. H(3,𝔽4) | D19 | semidirect |
| 120. #124 | C2×D19 | semidirect |
| 121. #124 | C2×D19 | semidirect |
| 129. #120 | C2×D19 | semidirect |
| 134. C19 | #3549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927286 | 2 |
| #11927256 | 2 |
| #11927176 | 2 |
| #11927112 | 2 |
| #11927109 | 2 |
| #11927093 | 2 |
| C19×H(3,𝔽4) | 2 |
| #3549 | 19 |