Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 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. #20245625 | C2 | semidirect |
| 3. #20245535 | C2 | semidirect |
| 4. #20242902 | C2 | semidirect |
| 5. #20241430 | C2 | semidirect |
| 6. #20241347 | C2 | semidirect |
| 7. C47×#1333 | C2 | semidirect |
| 10. #15689528 | C22 | semidirect |
| 19. C4⋊(C47⋊C16) | C22 | semidirect |
| 25. C47×#346 | C22 | semidirect |
| 26. C47×#334 | C22 | semidirect |
| 79. D8×C47 | SD16 | semidirect |
| 166. #1333 | D47 | semidirect |
| 190. #346 | C2×D47 | semidirect |
| 191. #334 | C2×D47 | semidirect |
| 193. C47 | #12378 | semidirect |
| 253. D8 | #10625325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254998 | 2 |
| #20245625 | 2 |
| #20245535 | 2 |
| #20242902 | 2 |
| #20241430 | 2 |
| #20241347 | 2 |
| C47×#1333 | 2 |
| #12378 | 47 |