Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
222 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 25. #13093970 | C8 | semidirect |
| 122. C47 | #12044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13093970 | 2 |
| C8×Dic188 | 2 |
| #20241461 | 2 |
| #20241352 | 2 |
| #20241351 | 2 |
| #20241305 | 2 |
| C8×Q16×C47 | 2 |
| #12044 | 47 |