Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
458 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 2. C4×C4⋊(C47⋊C8) | C2 | semidirect |
| 3. #20241213 | C2 | semidirect |
| 5. C47×#1745 | C2 | semidirect |
| 166. #1745 | D47 | semidirect |
| 194. C47 | #7676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251760 | 2 |
| C4×C4⋊(C47⋊C8) | 2 |
| #20241213 | 2 |
| #20241208 | 2 |
| C47×#1745 | 2 |
| #7676 | 47 |