Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 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 | C23×Q8×C19 | C2 |
| prime radical | C2×#10597376 | C2 |
| hypercenter | C23×Q8 | D19 |
| hypocenter | C19 | #2436 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597393 | C2 | semidirect |
| 3. #11926455 | C2 | semidirect |
| 4. #11926451 | C2 | semidirect |
| 5. #11926423 | C2 | semidirect |
| 6. C4×C22⋊Dic19 | C2 | semidirect |
| 7. C23×Q8×C19 | C2 | semidirect |
| 32. C2×Q8×C19 | D4 | semidirect |
| 82. C22×C19 | #124 | semidirect |
| 96. C23×Q8 | D19 | semidirect |
| 126. C19 | #2436 | semidirect |
| 134. C2×Q8 | C22⋊D19 | semidirect |
| 187. C22 | #10597393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597393 | 2 |
| C2×#10597376 | 2 |
| #11926455 | 2 |
| #11926451 | 2 |
| #11926423 | 2 |
| C4×C22⋊Dic19 | 2 |
| C23×Q8×C19 | 2 |
| #2436 | 19 |