Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1564 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 197 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×#379 | C2 |
| hypercenter | #379 | D19 |
| hypocenter | C19 | #2403 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D19 | C2 | semidirect |
| 2. C2×#10597328 | C2 | semidirect |
| 3. #11926453 | C2 | semidirect |
| 4. #11926421 | C2 | semidirect |
| 5. C19×#379 | C2 | semidirect |
| 7. C24×D19 | C22 | semidirect |
| 11. C22×C22⋊D19 | C22 | semidirect |
| 12. C23×Dic19 | C22 | semidirect |
| 13. C22×D76 | C22 | semidirect |
| 14. C2×C22⋊C4×C19 | C22 | semidirect |
| 15. C2×C22⋊C4×C19 | C22 | semidirect |
| 16. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 18. C19⋊#95 | C22 | semidirect |
| 21. C24×C19 | D4 | semidirect |
| 36. C2×C22⋊D19 | D4 | semidirect |
| 64. C22×D19 | C2×D4 | semidirect |
| 72. C2×Dic19 | C2×D4 | semidirect |
| 82. C22×C19 | #120 | semidirect |
| 98. #379 | D19 | semidirect |
| 115. C2×C22⋊C4 | C2×D19 | semidirect |
| 116. C2×C22⋊C4 | C2×D19 | semidirect |
| 118. C19 | #2403 | semidirect |
| 126. C24 | D76 | semidirect |
| 187. C22 | #10597328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D19 | 2 |
| C2×#10597328 | 2 |
| #11926453 | 2 |
| #11926421 | 2 |
| C19×#379 | 2 |
| #2403 | 19 |