Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1946 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1946 conjugacy classes of subgroups — too many to draw. Only its 259 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. #20252017 | C2 | semidirect |
| 3. #20244226 | C2 | semidirect |
| 4. #20243309 | C2 | semidirect |
| 5. #20243308 | C2 | semidirect |
| 6. C47×#1783 | C2 | semidirect |
| 16. #15689146 | C22 | semidirect |
| 17. C2×#13093941 | C22 | semidirect |
| 18. C2×#13093940 | C22 | semidirect |
| 20. M16×Dic47 | C22 | semidirect |
| 22. C2×#100×C47 | C22 | semidirect |
| 137. C2×Dic47 | #100 | semidirect |
| 170. #1783 | D47 | semidirect |
| 190. C2×#100 | C2×D47 | semidirect |
| 194. C47 | #21797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13094020 | 2 |
| #20252017 | 2 |
| #20244226 | 2 |
| #20243309 | 2 |
| #20243308 | 2 |
| C47×#1783 | 2 |
| #21797 | 47 |