Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
574 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20254310 | C2 | semidirect |
| 2. #20253848 | C2 | semidirect |
| 3. #20244376 | C2 | semidirect |
| 4. #20241980 | C2 | semidirect |
| 5. #20241805 | C2 | semidirect |
| 6. #20241277 | C2 | semidirect |
| 219. C47 | #10106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254310 | 2 |
| #20253848 | 2 |
| #20244376 | 2 |
| #20241980 | 2 |
| #20241805 | 2 |
| #20241277 | 2 |
| C47×#3253 | 2 |
| #10106 | 47 |