Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20245748 | C2 | semidirect |
| 3. #20241896 | C2 | semidirect |
| 4. #20241832 | C2 | semidirect |
| 5. #20241282 | C2 | semidirect |
| 6. #20241244 | C2 | semidirect |
| 7. C47×#1980 | C2 | semidirect |
| 11. #15689410 | C4 | semidirect |
| 12. #15689315 | C4 | semidirect |
| 45. C4⋊(C47⋊C8) | C2×C4 | semidirect |
| 58. C4⋊Q8×C47 | C2×C4 | semidirect |
| 59. #127×C47 | C2×C4 | semidirect |
| 158. D188 | #104 | semidirect |
| 192. #1980 | D47 | semidirect |
| 225. C47 | #9325 | semidirect |
| 232. C4⋊Q8 | C4×D47 | semidirect |
| 233. #127 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253475 | 2 |
| #20245748 | 2 |
| #20241896 | 2 |
| #20241832 | 2 |
| #20241282 | 2 |
| #20241244 | 2 |
| C47×#1980 | 2 |
| #9325 | 47 |