Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#10597336 | C2 | semidirect |
| 3. #11926911 | C2 | semidirect |
| 4. #11926907 | C2 | semidirect |
| 5. #11926900 | C2 | semidirect |
| 6. #11926897 | C2 | semidirect |
| 7. #11926546 | C2 | semidirect |
| 8. #11926545 | C2 | semidirect |
| 9. #11926543 | C2 | semidirect |
| 10. M16×Dic19 | C2 | semidirect |
| 11. C19×#417 | C2 | semidirect |
| 150. #417 | D19 | semidirect |
| 189. C19 | #3142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927090 | 2 |
| C2×#10597336 | 2 |
| #11926911 | 2 |
| #11926907 | 2 |
| #11926900 | 2 |
| #11926897 | 2 |
| #11926546 | 2 |
| #11926545 | 2 |
| #11926543 | 2 |
| M16×Dic19 | 2 |
| C19×#417 | 2 |
| #3142 | 19 |