Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
772 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20252436 | C2 | semidirect |
| 3. #20243318 | C2 | semidirect |
| 4. #20243308 | C2 | semidirect |
| 5. #20241294 | C2 | semidirect |
| 6. #20241264 | C2 | semidirect |
| 7. C47×#1513 | C2 | semidirect |
| 11. #15689273 | C4 | semidirect |
| 13. #15689256 | C4 | semidirect |
| 270. #1513 | D47 | semidirect |
| 307. C47 | #9520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252614 | 2 |
| #20252436 | 2 |
| #20243318 | 2 |
| #20243308 | 2 |
| #20241294 | 2 |
| #20241264 | 2 |
| C47×#1513 | 2 |
| #9520 | 47 |