Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
388 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 20. #15688939 | C4 | semidirect |
| 176. C47 | #12941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252256 | 2 |
| #20245174 | 2 |
| C2×#15688939 | 2 |
| #20244171 | 2 |
| #20241484 | 2 |
| #20241476 | 2 |
| C2×C47×#358 | 2 |
| #12941 | 47 |