Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
468 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20252464 | C2 | semidirect |
| 3. #20241812 | C2 | semidirect |
| 4. #20241728 | C2 | semidirect |
| 5. #20241299 | C2 | semidirect |
| 6. #20241249 | C2 | semidirect |
| 7. C47×#1557 | C2 | semidirect |
| 176. #1557 | D47 | semidirect |
| 208. C47 | #9529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253475 | 2 |
| #20252464 | 2 |
| #20241812 | 2 |
| #20241728 | 2 |
| #20241299 | 2 |
| #20241249 | 2 |
| C47×#1557 | 2 |
| #9529 | 47 |