Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
184 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20245270 | C2 | semidirect |
| 3. #20241591 | C2 | semidirect |
| 4. #20241572 | C2 | semidirect |
| 5. #20241571 | C2 | semidirect |
| 6. #20241522 | C2 | semidirect |
| 7. C47×#2178 | C2 | semidirect |
| 10. #15688963 | C4 | semidirect |
| 11. #15688961 | C4 | semidirect |
| 12. #15688960 | C4 | semidirect |
| 13. #15688958 | C4 | semidirect |
| 90. #2178 | D47 | semidirect |
| 114. C47 | #13656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245695 | 2 |
| #20245270 | 2 |
| #20241591 | 2 |
| #20241572 | 2 |
| #20241571 | 2 |
| #20241522 | 2 |
| C47×#2178 | 2 |
| #13656 | 47 |