Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
242 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20241461 | C2 | semidirect |
| 5. #20241460 | C2 | semidirect |
| 6. #20241459 | C2 | semidirect |
| 7. C47×#1372 | C2 | semidirect |
| 28. #13093963 | C8 | semidirect |
| 64. C16×C47 | C2×C8 | semidirect |
| 66. C47⋊C16 | C2×C8 | semidirect |
| 105. #1372 | D47 | semidirect |
| 127. C47 | #12009 | semidirect |
| 171. C16 | C8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13093963 | 2 |
| #20242135 | 2 |
| #335×D47 | 2 |
| #20241461 | 2 |
| #20241460 | 2 |
| #20241459 | 2 |
| C47×#1372 | 2 |
| #12009 | 47 |