Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 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. #11927280 | C2 | direct (N × H) |
| 2. C2×#10597382 | C2 | semidirect |
| 3. C2×#10597381 | C2 | semidirect |
| 4. C2×C4×Dic38 | C2 | semidirect |
| 5. C2×D4×Dic19 | C2 | semidirect |
| 15. #10597382 | C22 | semidirect |
| 16. #10597381 | C22 | semidirect |
| 17. D4×Dic19 | C22 | semidirect |
| 21. C4×Dic38 | C22 | semidirect |
| 75. C2×C19 | #559 | semidirect |
| 93. C19 | C2×#559 | semidirect |
| 140. C2 | #11927280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927280 | 2 |
| C2×#10597382 | 2 |
| C2×#10597381 | 2 |
| C2×C4×Dic38 | 2 |
| C2×D4×Dic19 | 2 |
| C2×C19×#127 | 2 |
| C2×#559 | 19 |