Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 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×#400 | C2 |
| prime radical | C23×D19 | C23 |
| hypercenter | #400 | D19 |
| hypocenter | C19 | #2627 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #400 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11926482 | C2 | semidirect |
| 4. #11926478 | C2 | semidirect |
| 5. #11926476 | C2 | semidirect |
| 6. #11926465 | C2 | semidirect |
| 7. #11926464 | C2 | semidirect |
| 11. C19×#400 | C2 | semidirect |
| 54. C2×C4×D19 | Q8 | semidirect |
| 127. #400 | D19 | semidirect |
| 166. C19 | #2627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597343 | 2 |
| C2×C4⋊C4×D19 | 2 |
| #11926482 | 2 |
| #11926478 | 2 |
| #11926476 | 2 |
| #11926465 | 2 |
| #11926464 | 2 |
| #11926418 | 2 |
| #11926406 | 2 |
| #11926403 | 2 |
| C19×#400 | 2 |
| #2627 | 19 |