Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
524 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20241299 | C2 | semidirect |
| 4. #20241298 | C2 | semidirect |
| 5. C47×#1307 | C2 | semidirect |
| 125. #1307 | D47 | semidirect |
| 145. C47 | #8120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252020 | 2 |
| #432×D47 | 2 |
| #20241299 | 2 |
| #20241298 | 2 |
| C47×#1307 | 2 |
| #8120 | 47 |