Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
390 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20245430 | C2 | semidirect |
| 3. #20242874 | C2 | semidirect |
| 4. #20241431 | C2 | semidirect |
| 5. #20241356 | C2 | semidirect |
| 6. #20241347 | C2 | semidirect |
| 7. C47×#2251 | C2 | semidirect |
| 18. C4⋊(C47⋊C16) | C22 | semidirect |
| 20. #15688874 | C22 | semidirect |
| 25. C47×#494 | C22 | semidirect |
| 26. C47×#346 | C22 | semidirect |
| 168. #2251 | D47 | semidirect |
| 186. #494 | C2×D47 | semidirect |
| 196. #346 | 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 |
|---|---|
| #20254997 | 2 |
| #20245430 | 2 |
| #20242874 | 2 |
| #20241431 | 2 |
| #20241356 | 2 |
| #20241347 | 2 |
| C47×#2251 | 2 |
| #12326 | 47 |