Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
452 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20256541 | C2 | semidirect |
| 2. #20245706 | C2 | semidirect |
| 3. #20245705 | C2 | semidirect |
| 4. #20245695 | C2 | semidirect |
| 5. C2×#15688963 | C2 | semidirect |
| 6. #20245682 | C2 | semidirect |
| 7. C47×#3417 | C2 | semidirect |
| 92. #3417 | D47 | semidirect |
| 118. C47 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256541 | 2 |
| #20245706 | 2 |
| #20245705 | 2 |
| #20245695 | 2 |
| C2×#15688963 | 2 |
| #20245682 | 2 |
| C47×#3417 | 2 |
| #33984 | 47 |