Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
498 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20252241 | C2 | semidirect |
| 3. #20245124 | C2 | semidirect |
| 4. #20245103 | C2 | semidirect |
| 5. #20241489 | C2 | semidirect |
| 6. #20241474 | C2 | semidirect |
| 7. C47×#1976 | C2 | semidirect |
| 12. C2×#13093967 | C4 | semidirect |
| 13. C2×#13093965 | C4 | semidirect |
| 45. C2×C47⋊C16 | C2×C4 | semidirect |
| 54. C2×Q16×C47 | C2×C4 | semidirect |
| 56. C2×D8×C47 | C2×C4 | semidirect |
| 172. #1976 | D47 | semidirect |
| 200. C47 | #13033 | semidirect |
| 207. C2×Q16 | C4×D47 | semidirect |
| 215. C2×D8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689558 | 2 |
| #20252241 | 2 |
| #20245124 | 2 |
| #20245103 | 2 |
| #20241489 | 2 |
| #20241474 | 2 |
| C47×#1976 | 2 |
| #13033 | 47 |