Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C19 |
| prime radical | C19×#459 | C2 |
| 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×#486 | C2 | semidirect |
| 2. C19×#461 | C2 | semidirect |
| 4. C19×#436 | C2 | semidirect |
| 5. C19×#334 | C2 | semidirect |
| 6. C19×#332 | C2 | semidirect |
| 7. C19×#331 | C2 | semidirect |
| 65. #1701 | C19 | direct (N × H) |
| 80. #486 | C2×C19 | semidirect |
| 81. #461 | C2×C19 | semidirect |
| 83. #436 | C2×C19 | semidirect |
| 84. #334 | C2×C19 | semidirect |
| 85. #332 | C2×C19 | semidirect |
| 86. #331 | C2×C19 | semidirect |
| 107. C19 | #1701 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#486 | 2 |
| C19×#461 | 2 |
| C19×#459 | 2 |
| C19×#436 | 2 |
| C19×#334 | 2 |
| C19×#332 | 2 |
| C19×#331 | 2 |
| #1701 | 19 |