Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
476 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 476 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 | C2×C19 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C19 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#576 | C2 | semidirect |
| 2. C19×#493 | C2 | semidirect |
| 3. C19×#472 | C2 | semidirect |
| 4. C19×#453 | C2 | semidirect |
| 5. C19×#443 | C2 | semidirect |
| 6. C19×H(5,𝔽2) | C22 | semidirect |
| 8. C19×AGL(1,ℤ/8) | C22 | semidirect |
| 12. C2×D8×C19 | C22 | semidirect |
| 13. C19×#131 | C22 | semidirect |
| 14. C19×#127 | C22 | semidirect |
| 15. C19×#108 | C22 | semidirect |
| 16. C19×#104 | C22 | semidirect |
| 17. C19×#100 | C22 | semidirect |
| 18. C4×C8×C19 | C22 | semidirect |
| 25. Q16×C19 | D4 | semidirect |
| 27. SD16×C19 | D4 | semidirect |
| 31. D8×C19 | D4 | semidirect |
| 52. #3292 | C19 | direct (N × H) |
| 61. #576 | C2×C19 | semidirect |
| 62. #493 | C2×C19 | semidirect |
| 63. #472 | C2×C19 | semidirect |
| 64. #453 | C2×C19 | semidirect |
| 65. #443 | C2×C19 | semidirect |
| 70. H(5,𝔽2) | C22×C19 | semidirect |
| 72. AGL(1,ℤ/8) | C22×C19 | semidirect |
| 76. C2×D8 | C22×C19 | semidirect |
| 77. #131 | C22×C19 | semidirect |
| 78. #127 | C22×C19 | semidirect |
| 79. #108 | C22×C19 | semidirect |
| 80. #104 | C22×C19 | semidirect |
| 81. #100 | C22×C19 | semidirect |
| 82. C4×C8 | C22×C19 | semidirect |
| 83. C19 | #3292 | direct (N × H) |
| 90. Q16 | D4×C19 | semidirect |
| 92. SD16 | D4×C19 | semidirect |
| 96. D8 | D4×C19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#576 | 2 |
| C19×#493 | 2 |
| C19×#472 | 2 |
| C19×#453 | 2 |
| C19×#443 | 2 |
| #3292 | 19 |