Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 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. #11926525 | C2 | semidirect |
| 3. #11926516 | C2 | semidirect |
| 4. #11926335 | C2 | semidirect |
| 5. #11926333 | C2 | semidirect |
| 6. #11926331 | C2 | semidirect |
| 7. C19×AΣL(1,𝔽16) | C2 | semidirect |
| 8. C23×Dic19 | C4 | semidirect |
| 11. #10597399 | C4 | semidirect |
| 16. #10597332 | C4 | semidirect |
| 20. #10597323 | C4 | semidirect |
| 124. AΣL(1,𝔽16) | D19 | semidirect |
| 150. C19 | #2120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927050 | 2 |
| #11926525 | 2 |
| #11926516 | 2 |
| #11926335 | 2 |
| #11926333 | 2 |
| #11926331 | 2 |
| C19×AΣL(1,𝔽16) | 2 |
| #2120 | 19 |