Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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×#10597365 | C2 | semidirect |
| 2. #11927213 | C2 | semidirect |
| 3. #11926919 | C2 | semidirect |
| 4. #11926780 | C2 | semidirect |
| 5. #11926777 | C2 | semidirect |
| 6. #11926742 | C2 | semidirect |
| 7. #11926689 | C2 | semidirect |
| 8. #11926688 | C2 | semidirect |
| 9. Q16×Dic19 | C2 | semidirect |
| 10. C8×C22⋊D19 | C2 | semidirect |
| 11. C2×C19×#135 | C2 | semidirect |
| 59. Q16×C19 | D4 | semidirect |
| 135. Dic19 | #135 | semidirect |
| 137. C2×#135 | D19 | semidirect |
| 183. C19 | #3287 | semidirect |
| 202. Q16 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597365 | 2 |
| #11927213 | 2 |
| #11926919 | 2 |
| #11926780 | 2 |
| #11926777 | 2 |
| #11926742 | 2 |
| #11926689 | 2 |
| #11926688 | 2 |
| Q16×Dic19 | 2 |
| C8×C22⋊D19 | 2 |
| C2×C19×#135 | 2 |
| #3287 | 19 |