Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #20245602 | C2 | semidirect |
| 3. #20245162 | C2 | semidirect |
| 4. C2×#15688935 | C2 | semidirect |
| 5. #20245009 | C2 | semidirect |
| 6. C47×#2916 | C2 | semidirect |
| 14. #15688947 | C22 | semidirect |
| 16. #15688905 | C22 | semidirect |
| 20. C47×#430 | C22 | semidirect |
| 127. #2916 | D47 | semidirect |
| 145. #430 | C2×D47 | semidirect |
| 153. C47 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253036 | 2 |
| #20245602 | 2 |
| #20245162 | 2 |
| C2×#15688935 | 2 |
| #20245009 | 2 |
| C47×#2916 | 2 |
| #33657 | 47 |