Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1068 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
| prime radical | C25×C19 | C22 |
| hypercenter | #379 | D19 |
| hypocenter | C19 | #2848 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#10597324 | C2 | semidirect |
| 3. #11926419 | C2 | semidirect |
| 4. #11926416 | C2 | semidirect |
| 5. #11926402 | C2 | semidirect |
| 12. C22×Dic38 | C22 | semidirect |
| 17. C2×C4⋊Dic19 | C22 | semidirect |
| 18. C2×Dic19⋊C4 | C22 | semidirect |
| 19. C2×Dic19⋊C4 | C22 | semidirect |
| 21. C19⋊#95 | C22 | semidirect |
| 24. C24×C19 | Q8 | semidirect |
| 72. C22×C19 | C22⋊Q8 | semidirect |
| 107. C19 | #2848 | semidirect |
| 110. C24 | Dic38 | semidirect |
| 157. C22 | #10597324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic19 | 2 |
| C2×#10597324 | 2 |
| #11926419 | 2 |
| #11926416 | 2 |
| #11926402 | 2 |
| #11926400 | 2 |
| C19×#379 | 2 |
| #2848 | 19 |