Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
| 3. #20242748 | C2 | semidirect |
| 4. #20241443 | C2 | semidirect |
| 5. Q8⋊(C47⋊C16) | C2 | semidirect |
| 6. #20241349 | C2 | semidirect |
| 7. Q8×D8×C47 | C2 | semidirect |
| 65. D8×C47 | SD16 | semidirect |
| 92. Q8×C47 | D16 | semidirect |
| 132. Q8×D8 | D47 | semidirect |
| 161. C47 | #12352 | semidirect |
| 206. D8 | #10625336 | semidirect |
| 229. Q8 | #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 |
| #20242748 | 2 |
| #20241443 | 2 |
| Q8⋊(C47⋊C16) | 2 |
| #20241349 | 2 |
| Q8×D8×C47 | 2 |
| #12352 | 47 |