Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
500 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20253511 | C2 | semidirect |
| 3. #20253415 | C2 | semidirect |
| 4. #20241856 | C2 | semidirect |
| 5. #20241731 | C2 | semidirect |
| 6. #20241249 | C2 | semidirect |
| 7. C47×#1536 | C2 | semidirect |
| 194. #1536 | D47 | semidirect |
| 229. C47 | #10040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254379 | 2 |
| #20253511 | 2 |
| #20253415 | 2 |
| #20241856 | 2 |
| #20241731 | 2 |
| #20241249 | 2 |
| C47×#1536 | 2 |
| #10040 | 47 |