Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#15689161 | C2 | semidirect |
| 2. #20245593 | C2 | semidirect |
| 3. #20245576 | C2 | semidirect |
| 4. #20245177 | C2 | semidirect |
| 5. #20245100 | C2 | semidirect |
| 6. #20244999 | C2 | semidirect |
| 14. #15688950 | C22 | semidirect |
| 15. #15688948 | C22 | semidirect |
| 16. #15688927 | C22 | semidirect |
| 17. #15688924 | C22 | semidirect |
| 170. C47 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689161 | 2 |
| #20245593 | 2 |
| #20245576 | 2 |
| #20245177 | 2 |
| #20245100 | 2 |
| #20244999 | 2 |
| C47×#3050 | 2 |
| #33647 | 47 |