Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20252403 | C2 | semidirect |
| 3. #20243201 | C2 | semidirect |
| 4. #20241896 | C2 | semidirect |
| 5. #20241282 | C2 | semidirect |
| 6. #20241260 | C2 | semidirect |
| 7. C47×#1525 | C2 | semidirect |
| 10. #15689405 | C4 | semidirect |
| 11. #15689400 | C4 | semidirect |
| 12. #15689320 | C4 | semidirect |
| 13. #15689315 | C4 | semidirect |
| 200. #1525 | D47 | semidirect |
| 235. C47 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253533 | 2 |
| #20252403 | 2 |
| #20243201 | 2 |
| #20241896 | 2 |
| #20241282 | 2 |
| #20241260 | 2 |
| C47×#1525 | 2 |
| #9161 | 47 |