Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
756 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 213 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×M16×D19 | C2 | semidirect |
| 3. #11926525 | C2 | direct (N × H) |
| 4. C2×#10597281 | C2 | semidirect |
| 5. C2×#10597290 | C2 | semidirect |
| 6. C2×C19×#100 | C2 | semidirect |
| 20. M16×D19 | C22 | semidirect |
| 23. C19×#100 | C22 | semidirect |
| 24. #10597290 | C22 | semidirect |
| 25. #10597281 | C22 | semidirect |
| 119. C2×#100 | D19 | semidirect |
| 123. C2×C19 | #413 | semidirect |
| 144. #100 | C2×D19 | semidirect |
| 145. C19 | C2×#413 | semidirect |
| 237. C2 | #11926525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64543 | 2 |
| C2×M16×D19 | 2 |
| #11926525 | 2 |
| C2×#10597281 | 2 |
| C2×#10597290 | 2 |
| C2×C19×#100 | 2 |
| C2×#413 | 19 |