Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
492 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20244997 | C2 | semidirect |
| 3. #341×D47 | C2 | semidirect |
| 4. #20241404 | C2 | semidirect |
| 5. #20241403 | C2 | semidirect |
| 6. #20241402 | C2 | semidirect |
| 7. C47×#1349 | C2 | semidirect |
| 20. C22⋊(C47⋊C16) | C22 | semidirect |
| 22. #15688888 | C22 | semidirect |
| 25. C47×C22⋊C16 | C22 | semidirect |
| 26. C47×#341 | C22 | semidirect |
| 190. #1349 | D47 | semidirect |
| 214. C22⋊C16 | C2×D47 | semidirect |
| 217. #341 | C2×D47 | semidirect |
| 218. C47 | #11711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D47 | 2 |
| #20244997 | 2 |
| #341×D47 | 2 |
| #20241404 | 2 |
| #20241403 | 2 |
| #20241402 | 2 |
| C47×#1349 | 2 |
| #11711 | 47 |