Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
346 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #20245613 | C2 | semidirect |
| 2. #20245423 | C2 | semidirect |
| 3. #20242743 | C2 | semidirect |
| 4. #20241443 | C2 | semidirect |
| 5. #20241349 | C2 | semidirect |
| 6. D4⋊(C47⋊C16) | C2 | semidirect |
| 7. C47×#3334 | C2 | semidirect |
| 97. D4×C47 | D16 | semidirect |
| 138. #3334 | D47 | semidirect |
| 168. C47 | #12340 | semidirect |
| 246. D4 | #13093965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245613 | 2 |
| #20245423 | 2 |
| #20242743 | 2 |
| #20241443 | 2 |
| #20241349 | 2 |
| D4⋊(C47⋊C16) | 2 |
| C47×#3334 | 2 |
| #12340 | 47 |