Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20245849 | C2 | semidirect |
| 3. #20244217 | C2 | semidirect |
| 4. #20241814 | C2 | semidirect |
| 5. #20241291 | C2 | semidirect |
| 6. #20241220 | C2 | semidirect |
| 7. C47×#1502 | C2 | semidirect |
| 11. #15689400 | C4 | semidirect |
| 12. #15689315 | C4 | semidirect |
| 126. C4×Dic47 | D8 | semidirect |
| 213. #1502 | D47 | semidirect |
| 245. C47 | #9237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253384 | 2 |
| #20245849 | 2 |
| #20244217 | 2 |
| #20241814 | 2 |
| #20241291 | 2 |
| #20241220 | 2 |
| C47×#1502 | 2 |
| #9237 | 47 |