Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
400 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 184 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C19 |
| prime radical | C22×D4×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#533 | C2 | semidirect |
| 3. C19×#489 | C2 | semidirect |
| 4. C19×#488 | C2 | semidirect |
| 5. C19×#419 | C2 | semidirect |
| 7. C4×M16×C19 | C2 | semidirect |
| 11. C19×C4⋊Q8 | C22 | semidirect |
| 12. C19×#125 | C22 | semidirect |
| 21. C19×#103 | C22 | semidirect |
| 23. C19×#97 | C22 | semidirect |
| 24. C4×C8×C19 | C22 | semidirect |
| 67. #3140 | C19 | direct (N × H) |
| 80. #533 | C2×C19 | semidirect |
| 82. #489 | C2×C19 | semidirect |
| 83. #488 | C2×C19 | semidirect |
| 84. #419 | C2×C19 | semidirect |
| 86. C4×M16 | C2×C19 | semidirect |
| 94. C4⋊Q8 | C22×C19 | semidirect |
| 95. #125 | C22×C19 | semidirect |
| 104. #103 | C22×C19 | semidirect |
| 106. #97 | C22×C19 | semidirect |
| 107. C4×C8 | C22×C19 | semidirect |
| 108. C19 | #3140 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#533 | 2 |
| C2×C19×#124 | 2 |
| C19×#489 | 2 |
| C19×#488 | 2 |
| C19×#419 | 2 |
| C19×#418 | 2 |
| C4×M16×C19 | 2 |
| #3140 | 19 |