Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20256522 | C2 | semidirect |
| 2. #20245116 | C2 | semidirect |
| 3. #20244281 | C2 | semidirect |
| 4. #20241468 | C2 | semidirect |
| 5. C47×#3150 | C2 | semidirect |
| 26. C2×Dic188 | D4 | semidirect |
| 28. C2×D376 | D4 | semidirect |
| 36. C2×C47⋊C16 | D4 | semidirect |
| 159. #3150 | D47 | semidirect |
| 186. C47 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256522 | 2 |
| #20245116 | 2 |
| #20244281 | 2 |
| #20241468 | 2 |
| C47×#3150 | 2 |
| #13340 | 47 |