Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. #20252411 | C2 | semidirect |
| 3. #20243377 | C2 | semidirect |
| 4. #20241813 | C2 | semidirect |
| 5. #20241248 | C2 | semidirect |
| 6. #20241247 | C2 | semidirect |
| 7. C47×#1486 | C2 | semidirect |
| 49. C4×C47⋊C8 | D4 | semidirect |
| 67. C4×C8×C47 | D4 | semidirect |
| 207. #1486 | D47 | semidirect |
| 236. C47 | #9485 | semidirect |
| 274. C4×C8 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252411 | 2 |
| #20248289 | 2 |
| #20243377 | 2 |
| #20241813 | 2 |
| #20241248 | 2 |
| #20241247 | 2 |
| C47×#1486 | 2 |
| #9485 | 47 |