Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1748 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1748 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×D19 |
| commutator, socle, cosocle | C22×C19 | C25 |
| Fitting | C4×#41×C19 | C2 |
| hypercenter | C4×#41 | D19 |
| hypocenter | C19 | #3498 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597435 | C2 | semidirect |
| 2. #11927216 | C2 | semidirect |
| 3. D4×D76 | C2 | semidirect |
| 4. #11927113 | C2 | semidirect |
| 5. #11927094 | C2 | semidirect |
| 6. C2×#10597320 | C2 | semidirect |
| 7. C4×#41×C19 | C2 | semidirect |
| 10. C2×#64545 | C22 | semidirect |
| 11. C2×D4×D19 | C22 | semidirect |
| 12. C2×#64541 | C22 | semidirect |
| 13. C22×D76 | C22 | semidirect |
| 14. C22×D76 | C22 | semidirect |
| 15. C4×Q8×C19 | C22 | semidirect |
| 16. C4×D4×C19 | C22 | semidirect |
| 17. C19×#117 | C22 | semidirect |
| 18. C2×C42×C19 | C22 | semidirect |
| 19. #10597376 | C22 | semidirect |
| 20. #10597341 | C22 | semidirect |
| 21. #10597328 | C22 | semidirect |
| 22. #10597321 | C22 | semidirect |
| 23. #10597320 | C22 | semidirect |
| 24. #10597320 | C22 | semidirect |
| 25. #10597320 | C22 | semidirect |
| 26. C4×D76 | C22 | semidirect |
| 27. #10597315 | C22 | semidirect |
| 29. #41×C19 | D4 | semidirect |
| 57. Q8×C19 | C2×D4 | semidirect |
| 58. D4×C19 | C2×D4 | semidirect |
| 60. C2×C4×C19 | C2×D4 | semidirect |
| 83. C4×C19 | H(5,𝔽2) | semidirect |
| 91. C4×#41 | D19 | semidirect |
| 111. C4×Q8 | C2×D19 | semidirect |
| 113. C4×D4 | C2×D19 | semidirect |
| 114. #117 | C2×D19 | semidirect |
| 115. C2×C42 | C2×D19 | semidirect |
| 116. C19 | #3498 | semidirect |
| 120. #41 | D76 | semidirect |
| 147. Q8 | C2×D76 | semidirect |
| 153. D4 | C2×D76 | semidirect |
| 157. C2×C4 | C2×D76 | semidirect |
| 172. C4 | #10597435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597435 | 2 |
| #11927216 | 2 |
| D4×D76 | 2 |
| #11927113 | 2 |
| #11927094 | 2 |
| C2×#10597320 | 2 |
| C4×#41×C19 | 2 |
| #3498 | 19 |