Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20252271 | C2 | semidirect |
| 3. #20245123 | C2 | semidirect |
| 4. C2×#15688932 | C2 | semidirect |
| 5. #20244284 | C2 | semidirect |
| 6. #20241475 | C2 | semidirect |
| 7. C47×#1386 | C2 | semidirect |
| 12. #15689566 | C4 | semidirect |
| 14. #15689561 | C4 | semidirect |
| 39. C2×Dic188 | C2×C4 | semidirect |
| 43. C2×D376 | C2×C4 | semidirect |
| 69. M32×C47 | C2×C4 | semidirect |
| 189. #1386 | D47 | semidirect |
| 218. C47 | #13030 | semidirect |
| 252. M32 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256524 | 2 |
| #20252271 | 2 |
| #20245123 | 2 |
| C2×#15688932 | 2 |
| #20244284 | 2 |
| #20241475 | 2 |
| C47×#1386 | 2 |
| #13030 | 47 |