Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20246201 | C2 | semidirect |
| 3. #20241985 | C2 | semidirect |
| 4. #20241935 | C2 | semidirect |
| 5. #20241253 | C2 | semidirect |
| 6. #20241244 | C2 | semidirect |
| 7. C47×#1980 | C2 | semidirect |
| 9. #15689510 | C4 | semidirect |
| 10. #15689485 | C4 | semidirect |
| 54. #13093935 | C2×C4 | semidirect |
| 63. C4⋊Q8×C47 | C2×C4 | semidirect |
| 64. #127×C47 | C2×C4 | semidirect |
| 217. #1980 | D47 | semidirect |
| 252. C47 | #9381 | semidirect |
| 260. C4⋊Q8 | C4×D47 | semidirect |
| 261. #127 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254371 | 2 |
| #20246201 | 2 |
| #20241985 | 2 |
| #20241935 | 2 |
| #20241253 | 2 |
| #20241244 | 2 |
| C47×#1980 | 2 |
| #9381 | 47 |