Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
402 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20245322 | C2 | semidirect |
| 3. #20244507 | C2 | semidirect |
| 4. #20241407 | C2 | semidirect |
| 5. #20241403 | C2 | semidirect |
| 6. #20241313 | C2 | semidirect |
| 7. C47×#2185 | C2 | semidirect |
| 174. #2185 | D47 | semidirect |
| 204. C47 | #12113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254284 | 2 |
| #20245322 | 2 |
| #20244507 | 2 |
| #20241407 | 2 |
| #20241403 | 2 |
| #20241313 | 2 |
| C47×#2185 | 2 |
| #12113 | 47 |