Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
510 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20243164 | C2 | semidirect |
| 3. #20241909 | C2 | semidirect |
| 5. #20241753 | C2 | semidirect |
| 7. C47×#1810 | C2 | semidirect |
| 8. C22×#10625325 | C4 | semidirect |
| 15. C2×#13093956 | C4 | semidirect |
| 16. C2×#13093949 | C4 | semidirect |
| 17. C2×#13093946 | C4 | semidirect |
| 210. #1810 | D47 | semidirect |
| 246. C47 | #9816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689352 | 2 |
| #20243164 | 2 |
| #20241909 | 2 |
| #20241905 | 2 |
| #20241753 | 2 |
| #20241749 | 2 |
| C47×#1810 | 2 |
| #9816 | 47 |