Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C2×#10597355 | C2 | semidirect |
| 2. C2×#10597388 | C2 | semidirect |
| 3. C2×#10597397 | C2 | semidirect |
| 5. C2×#10597390 | C2 | semidirect |
| 6. #11926937 | C2 | semidirect |
| 7. #11926935 | C2 | semidirect |
| 8. #11926922 | C2 | semidirect |
| 9. #11926915 | C2 | semidirect |
| 10. M16×Dic19 | C2 | semidirect |
| 11. C2×C19×#137 | C2 | semidirect |
| 70. M16×C19 | D4 | semidirect |
| 84. #64520 | D4 | semidirect |
| 141. Dic19 | #137 | semidirect |
| 145. C2×#137 | D19 | semidirect |
| 189. C19 | #3152 | semidirect |
| 224. M16 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597355 | 2 |
| C2×#10597388 | 2 |
| C2×#10597397 | 2 |
| #11927090 | 2 |
| C2×#10597390 | 2 |
| #11926937 | 2 |
| #11926935 | 2 |
| #11926922 | 2 |
| #11926915 | 2 |
| M16×Dic19 | 2 |
| C2×C19×#137 | 2 |
| #3152 | 19 |