Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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. D4×C47⋊C16 | C2 | semidirect |
| 4. #20241459 | C2 | semidirect |
| 5. #20241443 | C2 | semidirect |
| 6. #20241433 | C2 | semidirect |
| 7. C47×#1673 | C2 | semidirect |
| 111. #1673 | D47 | semidirect |
| 136. C47 | #12467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245613 | 2 |
| D4×C47⋊C16 | 2 |
| #20242743 | 2 |
| #20241459 | 2 |
| #20241443 | 2 |
| #20241433 | 2 |
| C47×#1673 | 2 |
| #12467 | 47 |