Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
3422 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 3422 conjugacy classes of subgroups — too many to draw. Only its 245 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 | #2846 |
| 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. C25×D19 | C2 | semidirect |
| 2. C2×#10597328 | C2 | semidirect |
| 3. C2×#10597399 | C2 | semidirect |
| 4. #11926399 | C2 | semidirect |
| 5. C19×#379 | C2 | semidirect |
| 10. C22×C22⋊D19 | C22 | semidirect |
| 11. C22×D76 | C22 | semidirect |
| 12. C2×C22⋊C4×C19 | C22 | semidirect |
| 14. C2×C22⋊Dic19 | C22 | semidirect |
| 15. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 18. C24×C19 | D4 | semidirect |
| 25. C23×D19 | D4 | semidirect |
| 27. C23×D19 | C23 | semidirect |
| 28. C22×C4×C19 | C23 | semidirect |
| 31. C22×Dic19 | C23 | semidirect |
| 61. C22×C19 | #120 | semidirect |
| 69. C2×D19 | #120 | semidirect |
| 76. #379 | D19 | semidirect |
| 92. C2×C22⋊C4 | C2×D19 | semidirect |
| 93. C19 | #2846 | semidirect |
| 103. C24 | D76 | semidirect |
| 109. C22×C4 | C22×D19 | semidirect |
| 143. C22 | #10597328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D19 | 2 |
| C2×#10597328 | 2 |
| C2×#10597399 | 2 |
| #11926399 | 2 |
| C19×#379 | 2 |
| #2846 | 19 |