Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
636 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20256538 | C2 | semidirect |
| 2. #20255193 | C2 | semidirect |
| 3. #20245641 | C2 | semidirect |
| 4. #20245514 | C2 | semidirect |
| 5. #20245469 | C2 | semidirect |
| 6. #20245367 | C2 | semidirect |
| 7. #20245226 | C2 | semidirect |
| 8. C47×#2178 | C2 | semidirect |
| 141. #2178 | 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 |
|---|---|
| #20256538 | 2 |
| #20255193 | 2 |
| #20245641 | 2 |
| #20245514 | 2 |
| #20245469 | 2 |
| #20245367 | 2 |
| #20245226 | 2 |
| C47×#2178 | 2 |
| #33860 | 47 |