Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
390 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20245659 | C2 | semidirect |
| 3. #20245433 | C2 | semidirect |
| 4. #20242878 | C2 | semidirect |
| 5. #20241430 | C2 | semidirect |
| 6. #20241347 | C2 | semidirect |
| 7. C47×#1333 | C2 | semidirect |
| 14. #15689503 | C22 | semidirect |
| 21. C4⋊(C47⋊C16) | C22 | semidirect |
| 25. C47×#346 | C22 | semidirect |
| 26. C47×#334 | C22 | semidirect |
| 172. #1333 | D47 | semidirect |
| 196. #346 | C2×D47 | semidirect |
| 197. #334 | C2×D47 | semidirect |
| 199. C47 | #12326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254998 | 2 |
| #20245659 | 2 |
| #20245433 | 2 |
| #20242878 | 2 |
| #20241430 | 2 |
| #20241347 | 2 |
| C47×#1333 | 2 |
| #12326 | 47 |