Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
684 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 161 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. #20243243 | C2 | semidirect |
| 4. #20241271 | C2 | semidirect |
| 5. C47×#1296 | C2 | semidirect |
| 15. #15688866 | C4 | semidirect |
| 35. C4⋊(C47⋊C8) | C2×C4 | semidirect |
| 42. C4⋊C8×C47 | C2×C4 | semidirect |
| 141. #1296 | D47 | semidirect |
| 160. C47 | #8231 | semidirect |
| 184. C4⋊C8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245950 | 2 |
| #20243243 | 2 |
| C2×#15688866 | 2 |
| #20241271 | 2 |
| C47×#1296 | 2 |
| #8231 | 47 |