Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
536 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 536 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. #20243424 | C2 | semidirect |
| 3. #20243167 | C2 | semidirect |
| 4. #20241905 | C2 | semidirect |
| 5. #20241904 | C2 | semidirect |
| 6. #20241747 | C2 | semidirect |
| 7. C47×#1471 | C2 | semidirect |
| 8. C22×#10625334 | C4 | semidirect |
| 16. C2×#13093957 | C4 | semidirect |
| 17. C2×#13093945 | C4 | semidirect |
| 18. C2×#13093944 | C4 | semidirect |
| 223. #1471 | D47 | semidirect |
| 255. C47 | #9818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689357 | 2 |
| #20243424 | 2 |
| #20243167 | 2 |
| #20241905 | 2 |
| #20241904 | 2 |
| #20241747 | 2 |
| C47×#1471 | 2 |
| #9818 | 47 |