Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 99 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×#15688938 | C2 | semidirect |
| 4. #20245107 | C2 | semidirect |
| 6. #20241470 | C2 | semidirect |
| 7. C47×#1945 | C2 | semidirect |
| 160. #1945 | D47 | semidirect |
| 184. C47 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689507 | 2 |
| C2×#15688938 | 2 |
| C2×#15688935 | 2 |
| #20245107 | 2 |
| #20245103 | 2 |
| #20241470 | 2 |
| C47×#1945 | 2 |
| #13414 | 47 |