Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
558 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20253975 | C2 | semidirect |
| 3. #20245668 | C2 | semidirect |
| 4. #20245643 | C2 | semidirect |
| 5. #20245616 | C2 | semidirect |
| 6. #20245483 | C2 | semidirect |
| 7. #20245243 | C2 | semidirect |
| 8. C4×C16×D47 | C2 | semidirect |
| 9. C47×#2240 | C2 | semidirect |
| 113. C47⋊C16 | #41 | semidirect |
| 135. C4×D47 | SD32 | semidirect |
| 166. #2240 | D47 | semidirect |
| 200. C47 | #33736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253975 | 2 |
| #20253965 | 2 |
| #20245668 | 2 |
| #20245643 | 2 |
| #20245616 | 2 |
| #20245483 | 2 |
| #20245243 | 2 |
| C4×C16×D47 | 2 |
| C47×#2240 | 2 |
| #33736 | 47 |