Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
724 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 115 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. C4×#13093986 | C2 | semidirect |
| 3. #20244215 | C2 | semidirect |
| 4. #20241882 | C2 | semidirect |
| 5. #20241812 | C2 | semidirect |
| 6. #20241220 | C2 | semidirect |
| 7. C47×#1303 | C2 | semidirect |
| 13. #15689404 | C4 | semidirect |
| 14. #15689319 | C4 | semidirect |
| 34. #13094024 | C2×C4 | semidirect |
| 35. #13094021 | C2×C4 | semidirect |
| 71. C4⋊C8×C47 | C2×C4 | semidirect |
| 131. C4×Dic47 | D8 | semidirect |
| 174. D188 | #104 | semidirect |
| 219. #1303 | D47 | semidirect |
| 249. C47 | #9233 | semidirect |
| 285. C4⋊C8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253389 | 2 |
| C4×#13093986 | 2 |
| #20244215 | 2 |
| #20241882 | 2 |
| #20241812 | 2 |
| #20241220 | 2 |
| C47×#1303 | 2 |
| #9233 | 47 |