Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
438 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #100×D19 | C2 | semidirect |
| 3. #99×D19 | C2 | semidirect |
| 4. #11926332 | C2 | semidirect |
| 5. #11926331 | C2 | semidirect |
| 6. #11926330 | C2 | semidirect |
| 7. C19×AΣL(1,𝔽16) | C2 | semidirect |
| 8. C24×D19 | C4 | semidirect |
| 12. #10597399 | C4 | semidirect |
| 17. #10597328 | C4 | semidirect |
| 20. C22⋊C4×D19 | C4 | semidirect |
| 21. C19×#100 | C22 | semidirect |
| 22. C19×#99 | C22 | semidirect |
| 23. #10597291 | C22 | semidirect |
| 24. #10597290 | C22 | semidirect |
| 27. C24×C19 | C2×C4 | semidirect |
| 34. C23×D19 | C2×C4 | semidirect |
| 53. C22⋊C4×C19 | C2×C4 | semidirect |
| 56. C22⋊Dic19 | C2×C4 | semidirect |
| 154. AΣL(1,𝔽16) | D19 | direct (N × H) |
| 164. D19 | AΣL(1,𝔽16) | direct (N × H) |
| 180. #100 | C2×D19 | semidirect |
| 183. #99 | C2×D19 | semidirect |
| 184. C19 | C2×AΣL(1,𝔽16) | semidirect |
| 193. C24 | C4×D19 | semidirect |
| 221. C22⋊C4 | C4×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #120×D19 | 2 |
| #100×D19 | 2 |
| #99×D19 | 2 |
| #11926332 | 2 |
| #11926331 | 2 |
| #11926330 | 2 |
| C19×AΣL(1,𝔽16) | 2 |
| C2×AΣL(1,𝔽16) | 19 |