Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
398 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 7. #15689528 | C4 | semidirect |
| 27. #13093958 | Q8 | semidirect |
| 113. C47 | #13275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689528 | 2 |
| C4×#13093958 | 2 |
| #20241480 | 2 |
| C2×C47×C4⋊C16 | 2 |
| #13275 | 47 |