Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
390 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 123 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×Q8×Dic19 | C2 | semidirect |
| 3. #11926872 | C2 | semidirect |
| 5. #11926853 | C2 | semidirect |
| 6. #11926768 | C2 | semidirect |
| 8. Q16×Dic19 | C2 | semidirect |
| 9. #11926629 | C2 | semidirect |
| 10. #11926594 | C2 | semidirect |
| 11. C19×#451 | C2 | semidirect |
| 133. #451 | D19 | semidirect |
| 174. C19 | #3108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927080 | 2 |
| C2×Q8×Dic19 | 2 |
| #11926872 | 2 |
| #11926858 | 2 |
| #11926853 | 2 |
| #11926768 | 2 |
| #11926683 | 2 |
| Q16×Dic19 | 2 |
| #11926629 | 2 |
| #11926594 | 2 |
| C19×#451 | 2 |
| #3108 | 19 |