Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 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. #20245638 | C2 | semidirect |
| 2. #20245637 | C2 | semidirect |
| 3. #20245613 | C2 | semidirect |
| 4. #20243002 | C2 | semidirect |
| 5. #20242981 | C2 | semidirect |
| 6. #20241307 | C2 | semidirect |
| 7. C47×#2240 | C2 | semidirect |
| 97. C47⋊C8 | D16 | semidirect |
| 117. #2240 | D47 | semidirect |
| 142. C47 | #12525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245638 | 2 |
| #20245637 | 2 |
| #20245613 | 2 |
| #20243002 | 2 |
| #20242981 | 2 |
| #20241307 | 2 |
| C47×#2240 | 2 |
| #12525 | 47 |