Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
502 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20245142 | C2 | semidirect |
| 3. #20242135 | C2 | semidirect |
| 4. #20241435 | C2 | semidirect |
| 5. #20241434 | C2 | semidirect |
| 6. #20241433 | C2 | semidirect |
| 7. C47×#1361 | C2 | semidirect |
| 18. C4⋊(C47⋊C16) | C22 | semidirect |
| 20. #15688876 | C22 | semidirect |
| 23. C47×C4⋊C16 | C22 | semidirect |
| 24. C47×#335 | C22 | semidirect |
| 160. #1361 | D47 | semidirect |
| 180. C4⋊C16 | C2×D47 | semidirect |
| 182. #335 | C2×D47 | semidirect |
| 184. C47 | #11931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D47 | 2 |
| #20245142 | 2 |
| #20242135 | 2 |
| #20241435 | 2 |
| #20241434 | 2 |
| #20241433 | 2 |
| C47×#1361 | 2 |
| #11931 | 47 |