Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
298 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 4. #20241310 | C2 | semidirect |
| 5. #20241309 | C2 | semidirect |
| 6. #20241308 | C2 | semidirect |
| 7. C47×#1313 | C2 | semidirect |
| 26. #13093963 | C8 | semidirect |
| 53. C16×C47 | C2×C8 | semidirect |
| 55. C47⋊C16 | C2×C8 | semidirect |
| 85. #1313 | D47 | semidirect |
| 102. C47 | #11404 | semidirect |
| 137. C16 | C8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244981 | 2 |
| #322×D47 | 2 |
| #20241310 | 2 |
| #20241309 | 2 |
| #20241308 | 2 |
| C47×#1313 | 2 |
| #11404 | 47 |