Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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. C4×#13093959 | C2 | semidirect |
| 3. #20242149 | C2 | semidirect |
| 6. #20241259 | C2 | semidirect |
| 7. C47×#1291 | C2 | semidirect |
| 168. #1291 | D47 | semidirect |
| 197. C47 | #8690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252357 | 2 |
| C4×#13093959 | 2 |
| #20242149 | 2 |
| #20241996 | 2 |
| #20241993 | 2 |
| #20241259 | 2 |
| C47×#1291 | 2 |
| #8690 | 47 |