Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 89 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. #349×D47 | C2 | semidirect |
| 3. #20241324 | C2 | semidirect |
| 4. #20241323 | C2 | semidirect |
| 5. C47×#1320 | C2 | semidirect |
| 176. #1320 | D47 | semidirect |
| 197. C47 | #11436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251831 | 2 |
| #349×D47 | 2 |
| #20241324 | 2 |
| #20241323 | 2 |
| C47×#1320 | 2 |
| #11436 | 47 |