Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
240 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20242274 | C2 | semidirect |
| 3. #20241459 | C2 | semidirect |
| 4. #20241349 | C2 | semidirect |
| 5. #20241348 | C2 | semidirect |
| 6. #20241306 | C2 | semidirect |
| 7. C8×D8×C47 | C2 | semidirect |
| 49. D8×C47 | M16 | semidirect |
| 88. C8×C47 | D16 | semidirect |
| 109. C8×D8 | D47 | semidirect |
| 134. C47 | #12069 | semidirect |
| 163. D8 | #10625324 | semidirect |
| 201. C8 | #13093965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13093965 | 2 |
| #20242274 | 2 |
| #20241459 | 2 |
| #20241349 | 2 |
| #20241348 | 2 |
| #20241306 | 2 |
| C8×D8×C47 | 2 |
| #12069 | 47 |