Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #20256522 | C2 | semidirect |
| 2. C2×#15689561 | C2 | semidirect |
| 3. #20253875 | C2 | semidirect |
| 4. #20245103 | C2 | semidirect |
| 5. #20244284 | C2 | semidirect |
| 6. #20241475 | C2 | semidirect |
| 7. C47×#2145 | C2 | semidirect |
| 41. C2×Dic188 | D4 | semidirect |
| 50. C2×D376 | D4 | semidirect |
| 66. C2×C47⋊C16 | D4 | semidirect |
| 82. M32×C47 | D4 | semidirect |
| 214. #2145 | D47 | semidirect |
| 250. C47 | #13334 | semidirect |
| 295. M32 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256522 | 2 |
| C2×#15689561 | 2 |
| #20253875 | 2 |
| #20245103 | 2 |
| #20244284 | 2 |
| #20241475 | 2 |
| C47×#2145 | 2 |
| #13334 | 47 |