Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1024 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 469 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. #11927294 | C2 | direct (N × H) |
| 2. C2×#10597390 | C2 | semidirect |
| 3. C2×#10597325 | C2 | semidirect |
| 4. C2×#10597316 | C2 | semidirect |
| 6. C2×#10597324 | C2 | semidirect |
| 17. #10597390 | C22 | semidirect |
| 25. #10597325 | C22 | semidirect |
| 26. #10597324 | C22 | semidirect |
| 27. #10597316 | C22 | semidirect |
| 90. C2×C19 | #563 | semidirect |
| 113. C19 | C2×#563 | semidirect |
| 168. C2 | #11927294 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927294 | 2 |
| C2×#10597390 | 2 |
| C2×#10597325 | 2 |
| C2×#10597316 | 2 |
| C2×#10597381 | 2 |
| C2×#10597324 | 2 |
| C2×C19×#124 | 2 |
| C2×#563 | 19 |