Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 1. #11927259 | C2 | semidirect |
| 2. #11927199 | C2 | semidirect |
| 3. #11926895 | C2 | semidirect |
| 4. #11926886 | C2 | semidirect |
| 5. #11926835 | C2 | semidirect |
| 6. #11926773 | C2 | semidirect |
| 7. #11926750 | C2 | semidirect |
| 8. #11926691 | C2 | semidirect |
| 9. C4×D152 | C2 | semidirect |
| 10. #11926541 | C2 | semidirect |
| 11. C8×D4×C19 | C2 | semidirect |
| 134. C8×D4 | D19 | semidirect |
| 171. C19 | #3303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927259 | 2 |
| #11927199 | 2 |
| #11926895 | 2 |
| #11926886 | 2 |
| #11926835 | 2 |
| #11926773 | 2 |
| #11926750 | 2 |
| #11926691 | 2 |
| C4×D152 | 2 |
| #11926541 | 2 |
| C8×D4×C19 | 2 |
| #3303 | 19 |