Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
462 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#15688937 | C2 | semidirect |
| 3. C2×#15688931 | C2 | semidirect |
| 4. #20245101 | C2 | semidirect |
| 5. C2×#15688925 | C2 | semidirect |
| 6. #20244173 | C2 | semidirect |
| 7. C47×#1379 | C2 | semidirect |
| 54. #13093960 | D4 | semidirect |
| 189. #1379 | D47 | semidirect |
| 216. C47 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253874 | 2 |
| C2×#15688937 | 2 |
| C2×#15688931 | 2 |
| #20245101 | 2 |
| C2×#15688925 | 2 |
| #20244173 | 2 |
| C47×#1379 | 2 |
| #13411 | 47 |