Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
772 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 772 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. #20243320 | C2 | semidirect |
| 3. #20243308 | C2 | semidirect |
| 4. #20241931 | C2 | semidirect |
| 5. #20241293 | C2 | semidirect |
| 6. #20241265 | C2 | semidirect |
| 7. C47×#2976 | C2 | semidirect |
| 11. #15689273 | C4 | semidirect |
| 13. #15689256 | C4 | semidirect |
| 267. #2976 | 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 |
| #20243320 | 2 |
| #20243308 | 2 |
| #20241931 | 2 |
| #20241293 | 2 |
| #20241265 | 2 |
| C47×#2976 | 2 |
| #9520 | 47 |