Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
594 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#15689559 | C2 | semidirect |
| 2. #20253831 | C2 | semidirect |
| 3. C2×#15688934 | C2 | semidirect |
| 4. C2×#15688933 | C2 | semidirect |
| 5. #20244265 | C2 | semidirect |
| 6. #20241471 | C2 | semidirect |
| 7. C2×C47×#509 | C2 | semidirect |
| 60. #13093964 | D4 | semidirect |
| 81. C2×D8×C47 | D4 | semidirect |
| 86. M32×C47 | D4 | semidirect |
| 223. C2×#509 | D47 | semidirect |
| 261. C47 | #13341 | semidirect |
| 290. C2×D8 | C22⋊D47 | semidirect |
| 309. M32 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689559 | 2 |
| #20253831 | 2 |
| C2×#15688934 | 2 |
| C2×#15688933 | 2 |
| #20244265 | 2 |
| #20241471 | 2 |
| C2×C47×#509 | 2 |
| #13341 | 47 |