Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
570 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. #20254518 | C2 | semidirect |
| 2. #20254315 | C2 | semidirect |
| 4. #20244361 | C2 | semidirect |
| 5. #20241949 | C2 | semidirect |
| 6. #20241949 | C2 | semidirect |
| 7. C47×#1281 | C2 | semidirect |
| 105. C2×C8×C47 | SD16 | semidirect |
| 195. #1281 | D47 | semidirect |
| 226. C47 | #10221 | semidirect |
| 306. C2×C8 | #10625325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254518 | 2 |
| #20254315 | 2 |
| #20253834 | 2 |
| #20244361 | 2 |
| #20241949 | 2 |
| C47×#1281 | 2 |
| #10221 | 47 |