Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1000 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D19 |
| commutator, socle, cosocle | C23×C19 | C24 |
| Fitting | C19×#390 | C2 |
| hypercenter | #390 | D19 |
| hypocenter | C19 | #2679 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597328 | C2 | semidirect |
| 2. C2×#10597383 | C2 | semidirect |
| 3. #11926461 | C2 | semidirect |
| 4. #11926460 | C2 | semidirect |
| 5. #11926446 | C2 | semidirect |
| 6. C19×#390 | C2 | semidirect |
| 7. C24×D19 | C22 | semidirect |
| 12. C2×C4⋊C4×C19 | C22 | semidirect |
| 13. C2×C22⋊C4×C19 | C22 | semidirect |
| 14. C2×C42×C19 | C22 | semidirect |
| 15. C2×C22⋊Dic19 | C22 | semidirect |
| 17. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 18. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 19. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 20. C2×C4⋊Dic19 | C22 | semidirect |
| 22. C19⋊#95 | C22 | semidirect |
| 32. C2×D4×C19 | D4 | semidirect |
| 44. C2×D76 | D4 | semidirect |
| 114. #390 | D19 | semidirect |
| 130. C2×C4⋊C4 | C2×D19 | semidirect |
| 135. C2×C22⋊C4 | C2×D19 | semidirect |
| 136. C2×C42 | C2×D19 | semidirect |
| 138. C19 | #2679 | semidirect |
| 156. C2×D4 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597328 | 2 |
| C2×#10597383 | 2 |
| #11926461 | 2 |
| #11926460 | 2 |
| #11926446 | 2 |
| C19×#390 | 2 |
| #2679 | 19 |