Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20244315 | C2 | semidirect |
| 3. C2×#15688867 | C2 | semidirect |
| 4. #20241229 | C2 | semidirect |
| 5. C47×#2366 | C2 | semidirect |
| 9. #15689499 | C4 | semidirect |
| 29. #13094021 | C2×C4 | semidirect |
| 35. C4×C47⋊C8 | C2×C4 | semidirect |
| 82. C4⋊C4×C47 | D8 | semidirect |
| 164. #2366 | D47 | semidirect |
| 189. C47 | #9061 | semidirect |
| 259. C4⋊C4 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689499 | 2 |
| #20244315 | 2 |
| C2×#15688867 | 2 |
| #20241229 | 2 |
| C47×#2366 | 2 |
| #9061 | 47 |