Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1206 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 403 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. #20245750 | C2 | semidirect |
| 3. C4×#13093957 | C2 | semidirect |
| 4. #20243216 | C2 | semidirect |
| 5. #20243213 | C2 | semidirect |
| 6. #20243075 | C2 | semidirect |
| 7. C47×#2275 | C2 | semidirect |
| 10. C4×#10625334 | C4 | semidirect |
| 31. C4×D188 | C2×C4 | semidirect |
| 35. #13093957 | C2×C4 | semidirect |
| 36. #13093945 | C2×C4 | semidirect |
| 37. #13093944 | C2×C4 | semidirect |
| 39. C4×C47⋊C8 | C2×C4 | semidirect |
| 44. C4×D4×C47 | C2×C4 | semidirect |
| 73. #10625334 | C42 | semidirect |
| 125. #2275 | D47 | semidirect |
| 152. C47 | #20508 | semidirect |
| 163. C4×D4 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#10625334 | 2 |
| #20245750 | 2 |
| C4×#13093957 | 2 |
| #20243216 | 2 |
| #20243213 | 2 |
| #20243075 | 2 |
| C47×#2275 | 2 |
| #20508 | 47 |