Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
516 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20245123 | C2 | semidirect |
| 3. C2×#15688905 | C2 | semidirect |
| 4. #20241489 | C2 | semidirect |
| 5. C47×#2911 | C2 | semidirect |
| 9. #15689381 | C4 | semidirect |
| 10. #15689376 | C4 | semidirect |
| 24. C2×Dic188 | C2×C4 | semidirect |
| 26. C2×D376 | C2×C4 | semidirect |
| 37. #13093956 | C2×C4 | semidirect |
| 57. #106×C47 | D4 | semidirect |
| 157. #2911 | D47 | semidirect |
| 182. C47 | #13008 | semidirect |
| 217. #106 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252997 | 2 |
| #20245123 | 2 |
| C2×#15688905 | 2 |
| #20241489 | 2 |
| C47×#2911 | 2 |
| #13008 | 47 |