Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597396 | C2 | semidirect |
| 2. #11927215 | C2 | semidirect |
| 3. #11926920 | C2 | semidirect |
| 4. #11926778 | C2 | semidirect |
| 5. #11926744 | C2 | semidirect |
| 6. #11926741 | C2 | semidirect |
| 7. #11926689 | C2 | semidirect |
| 8. #11926687 | C2 | semidirect |
| 9. C4×#64528 | C2 | semidirect |
| 10. D4×C19⋊C8 | C2 | semidirect |
| 11. C19×#550 | C2 | semidirect |
| 69. #64528 | D4 | semidirect |
| 132. C4×C19 | #135 | semidirect |
| 139. #550 | D19 | semidirect |
| 184. C19 | #3287 | semidirect |
| 276. C4 | #10597396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597396 | 2 |
| #11927215 | 2 |
| #11926920 | 2 |
| #11926778 | 2 |
| #11926744 | 2 |
| #11926741 | 2 |
| #11926689 | 2 |
| #11926687 | 2 |
| C4×#64528 | 2 |
| D4×C19⋊C8 | 2 |
| C19×#550 | 2 |
| #3287 | 19 |