Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
522 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #20241221 | C2 | semidirect |
| 4. #20241216 | C2 | semidirect |
| 5. C47×#1276 | C2 | semidirect |
| 36. C42×D47 | C8 | semidirect |
| 148. #1276 | D47 | semidirect |
| 168. C47 | #8730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13093981 | 2 |
| #20241700 | 2 |
| #20241221 | 2 |
| #20241216 | 2 |
| C47×#1276 | 2 |
| #8730 | 47 |