Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 1. #11927078 | C2 | semidirect |
| 2. #11926844 | C2 | semidirect |
| 3. #11926836 | C2 | semidirect |
| 4. #11926831 | C2 | semidirect |
| 5. #11926778 | C2 | semidirect |
| 6. #11926771 | C2 | semidirect |
| 7. #11926759 | C2 | semidirect |
| 8. #11926741 | C2 | semidirect |
| 9. #11926736 | C2 | semidirect |
| 10. C2×C4⋊(C19⋊C8) | C2 | semidirect |
| 11. C19×#532 | C2 | semidirect |
| 136. #532 | D19 | semidirect |
| 184. C19 | #3247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927078 | 2 |
| #11926844 | 2 |
| #11926836 | 2 |
| #11926831 | 2 |
| #11926778 | 2 |
| #11926771 | 2 |
| #11926759 | 2 |
| #11926741 | 2 |
| #11926736 | 2 |
| C2×C4⋊(C19⋊C8) | 2 |
| C19×#532 | 2 |
| #3247 | 19 |