Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
240 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20242272 | C2 | semidirect |
| 3. D8×C47⋊C8 | C2 | semidirect |
| 4. #20241459 | C2 | semidirect |
| 5. #20241350 | C2 | semidirect |
| 6. #20241307 | C2 | semidirect |
| 7. C47×#1331 | C2 | semidirect |
| 49. D8×C47 | M16 | semidirect |
| 91. C47⋊C8 | D16 | semidirect |
| 112. #1331 | D47 | semidirect |
| 134. C47 | #12069 | semidirect |
| 163. D8 | #10625324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13093965 | 2 |
| #20242272 | 2 |
| D8×C47⋊C8 | 2 |
| #20241459 | 2 |
| #20241350 | 2 |
| #20241307 | 2 |
| C47×#1331 | 2 |
| #12069 | 47 |