Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
186 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C19 |
| prime radical | C19×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#500 | C2 | semidirect |
| 3. C19×#487 | C2 | semidirect |
| 4. C19×#487 | C2 | semidirect |
| 7. C19×#322 | C2 | semidirect |
| 54. #1719 | C19 | direct (N × H) |
| 65. #500 | C2×C19 | semidirect |
| 67. #487 | C2×C19 | semidirect |
| 68. #487 | C2×C19 | semidirect |
| 71. #322 | C2×C19 | semidirect |
| 89. C19 | #1719 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#500 | 2 |
| C19×#492 | 2 |
| C19×#487 | 2 |
| C19×#486 | 2 |
| C19×#322 | 2 |
| #1719 | 19 |