Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
496 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20245107 | C2 | semidirect |
| 4. #20244303 | C2 | semidirect |
| 5. #20241483 | C2 | semidirect |
| 6. #20241477 | C2 | semidirect |
| 11. C2×#13093968 | C4 | semidirect |
| 32. C2×Dic188 | C2×C4 | semidirect |
| 40. C2×C47⋊C16 | C2×C4 | semidirect |
| 186. C47 | #13019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093968 | 2 |
| C2×#15688936 | 2 |
| #20245107 | 2 |
| #20244303 | 2 |
| #20241483 | 2 |
| #20241477 | 2 |
| C47×#2948 | 2 |
| #13019 | 47 |