Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
238 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20241457 | C2 | semidirect |
| 4. #20241451 | C2 | semidirect |
| 106. C47 | #12016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C47⋊C16) | 2 |
| C8×#10625329 | 2 |
| #20241457 | 2 |
| #20241451 | 2 |
| C47×#2163 | 2 |
| #12016 | 47 |