Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
484 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20252159 | C2 | semidirect |
| 3. #20245117 | C2 | semidirect |
| 4. #20244277 | C2 | semidirect |
| 5. #20241504 | C2 | semidirect |
| 6. #20241469 | C2 | semidirect |
| 7. C47×#2145 | C2 | semidirect |
| 10. #15689564 | C4 | semidirect |
| 12. #15689559 | C4 | semidirect |
| 50. #13093964 | C2×C4 | semidirect |
| 66. C2×Q16×C47 | C2×C4 | semidirect |
| 68. C2×D8×C47 | C2×C4 | semidirect |
| 188. #2145 | D47 | semidirect |
| 220. C47 | #13027 | semidirect |
| 232. C2×Q16 | C4×D47 | semidirect |
| 236. C2×D8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256522 | 2 |
| #20252159 | 2 |
| #20245117 | 2 |
| #20244277 | 2 |
| #20241504 | 2 |
| #20241469 | 2 |
| C47×#2145 | 2 |
| #13027 | 47 |