Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
306 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20245612 | C2 | semidirect |
| 3. #20245611 | C2 | semidirect |
| 4. #20243005 | C2 | semidirect |
| 6. C16×C47⋊C8 | C2 | semidirect |
| 7. C47×#2240 | C2 | semidirect |
| 108. #2240 | D47 | semidirect |
| 132. C47 | #12509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245613 | 2 |
| #20245612 | 2 |
| #20245611 | 2 |
| #20243005 | 2 |
| #20243002 | 2 |
| C16×C47⋊C8 | 2 |
| C47×#2240 | 2 |
| #12509 | 47 |