Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20241358 | C2 | semidirect |
| 136. C47 | #11668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245191 | 2 |
| #20242151 | 2 |
| #20241358 | 2 |
| C2×C4×Q16×C47 | 2 |
| #11668 | 47 |