Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
328 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20256377 | C2 | semidirect |
| 2. #20245644 | C2 | semidirect |
| 4. #20242748 | C2 | semidirect |
| 5. #20241438 | C2 | semidirect |
| 6. #20241350 | C2 | semidirect |
| 7. C47×Q8⋊C16 | C2 | semidirect |
| 138. Q8⋊C16 | D47 | semidirect |
| 162. C47 | #12331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256377 | 2 |
| #20245644 | 2 |
| #20245424 | 2 |
| #20242748 | 2 |
| #20241438 | 2 |
| #20241350 | 2 |
| C47×Q8⋊C16 | 2 |
| #12331 | 47 |