Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
418 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20245613 | C2 | semidirect |
| 3. #20242784 | C2 | semidirect |
| 4. #20241435 | C2 | semidirect |
| 5. #20241349 | C2 | semidirect |
| 6. #20241342 | C2 | semidirect |
| 7. C47×#2226 | C2 | semidirect |
| 17. C4×C47⋊C16 | C22 | semidirect |
| 18. #15688876 | C22 | semidirect |
| 20. C47×#500 | C22 | semidirect |
| 23. C47×C4⋊C16 | C22 | semidirect |
| 146. #2226 | D47 | semidirect |
| 159. #500 | C2×D47 | semidirect |
| 168. C4⋊C16 | C2×D47 | semidirect |
| 174. C47 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D188 | 2 |
| #20245613 | 2 |
| #20242784 | 2 |
| #20241435 | 2 |
| #20241349 | 2 |
| #20241342 | 2 |
| C47×#2226 | 2 |
| #12372 | 47 |