Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q8×D376 | C2 | semidirect |
| 2. #20245611 | C2 | semidirect |
| 4. #20241444 | C2 | semidirect |
| 5. Q8⋊(C47⋊C16) | C2 | semidirect |
| 6. #20241348 | C2 | semidirect |
| 7. C47×#1668 | C2 | semidirect |
| 83. D376 | SD16 | semidirect |
| 89. Q8×C47 | D16 | semidirect |
| 135. #1668 | D47 | semidirect |
| 161. C47 | #12352 | semidirect |
| 229. Q8 | #13093965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D376 | 2 |
| #20245611 | 2 |
| #20245420 | 2 |
| #20241444 | 2 |
| Q8⋊(C47⋊C16) | 2 |
| #20241348 | 2 |
| C47×#1668 | 2 |
| #12352 | 47 |