Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 57. Q16×C47 | Q16 | semidirect |
| 142. C47 | #12405 | semidirect |
| 176. Q16 | Dic188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256277 | 2 |
| #20245663 | 2 |
| #20245530 | 2 |
| #20242783 | 2 |
| #20241444 | 2 |
| #20241368 | 2 |
| C47×#1332 | 2 |
| #12405 | 47 |