Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20245700 | C2 | semidirect |
| 2. #20245636 | C2 | semidirect |
| 3. #20245269 | C2 | semidirect |
| 4. #20241585 | C2 | semidirect |
| 5. #20241579 | C2 | semidirect |
| 6. #20241578 | C2 | semidirect |
| 7. C47×#2263 | C2 | semidirect |
| 37. Q32×C47 | D4 | semidirect |
| 41. D16×C47 | D4 | semidirect |
| 96. #2263 | D47 | semidirect |
| 122. C47 | #13692 | semidirect |
| 129. Q32 | C22⋊D47 | semidirect |
| 136. D16 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245700 | 2 |
| #20245636 | 2 |
| #20245269 | 2 |
| #20241585 | 2 |
| #20241579 | 2 |
| #20241578 | 2 |
| C47×#2263 | 2 |
| #13692 | 47 |