Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
488 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #20244209 | C2 | semidirect |
| 4. #20241952 | C2 | semidirect |
| 6. #20241232 | C2 | semidirect |
| 7. C47×#3229 | C2 | semidirect |
| 176. #3229 | D47 | semidirect |
| 212. C47 | #10226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254509 | 2 |
| #20253736 | 2 |
| #20244209 | 2 |
| #20241952 | 2 |
| #20241949 | 2 |
| #20241232 | 2 |
| C47×#3229 | 2 |
| #10226 | 47 |