Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
598 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 598 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 |
|---|---|---|
| 2. #20253506 | C2 | semidirect |
| 3. #20249251 | C2 | semidirect |
| 4. #20242011 | C2 | semidirect |
| 5. #20241834 | C2 | semidirect |
| 6. #20241252 | C2 | semidirect |
| 7. C47×#1514 | C2 | semidirect |
| 211. #1514 | D47 | semidirect |
| 245. C47 | #10020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253856 | 2 |
| #20253506 | 2 |
| #20249251 | 2 |
| #20242011 | 2 |
| #20241834 | 2 |
| #20241252 | 2 |
| C47×#1514 | 2 |
| #10020 | 47 |