Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
474 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20241985 | C2 | semidirect |
| 3. #20241822 | C2 | semidirect |
| 4. #20241741 | C2 | semidirect |
| 5. #20241298 | C2 | semidirect |
| 6. #20241278 | C2 | semidirect |
| 7. C47×#2970 | C2 | semidirect |
| 203. #2970 | D47 | semidirect |
| 240. C47 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252882 | 2 |
| #20241985 | 2 |
| #20241822 | 2 |
| #20241741 | 2 |
| #20241298 | 2 |
| #20241278 | 2 |
| C47×#2970 | 2 |
| #9349 | 47 |