Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 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×#15689558 | C2 | semidirect |
| 2. C2×#15689393 | C2 | semidirect |
| 3. C2×#15688930 | C2 | semidirect |
| 4. C2×#15688923 | C2 | semidirect |
| 5. C2×#15688907 | C2 | semidirect |
| 6. #20241496 | C2 | semidirect |
| 7. C47×#3061 | C2 | semidirect |
| 40. C2×D376 | D4 | semidirect |
| 46. #13093964 | D4 | semidirect |
| 52. #13093960 | D4 | semidirect |
| 213. #3061 | D47 | semidirect |
| 249. C47 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689558 | 2 |
| C2×#15689393 | 2 |
| C2×#15688930 | 2 |
| C2×#15688923 | 2 |
| C2×#15688907 | 2 |
| #20241496 | 2 |
| C47×#3061 | 2 |
| #13307 | 47 |