Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
760 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20244372 | C2 | semidirect |
| 4. #20241907 | C2 | semidirect |
| 5. #20241294 | C2 | semidirect |
| 6. #20241274 | C2 | semidirect |
| 8. C2×#13094054 | C4 | semidirect |
| 14. #15689124 | C4 | semidirect |
| 29. C22×Dic94 | C2×C4 | semidirect |
| 34. C2×#10625329 | C2×C4 | semidirect |
| 39. C2×C4⋊Dic47 | C2×C4 | semidirect |
| 255. C47 | #9361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252648 | 2 |
| #20244372 | 2 |
| #20243332 | 2 |
| #20241907 | 2 |
| #20241294 | 2 |
| #20241274 | 2 |
| C47×#2339 | 2 |
| #9361 | 47 |