Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
636 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 636 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. #20256541 | C2 | semidirect |
| 2. #20255193 | C2 | semidirect |
| 3. #20245641 | C2 | semidirect |
| 4. #20245513 | C2 | semidirect |
| 5. #20245470 | C2 | semidirect |
| 6. #20245368 | C2 | semidirect |
| 7. #20245270 | C2 | semidirect |
| 8. C47×#2170 | C2 | semidirect |
| 142. #2170 | D47 | semidirect |
| 169. C47 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256541 | 2 |
| #20255193 | 2 |
| #20245641 | 2 |
| #20245513 | 2 |
| #20245470 | 2 |
| #20245368 | 2 |
| #20245270 | 2 |
| C47×#2170 | 2 |
| #33860 | 47 |