Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
178 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20241589 | C2 | semidirect |
| 3. #20241587 | C2 | semidirect |
| 4. #20241565 | C2 | semidirect |
| 5. #20241565 | C2 | semidirect |
| 6. C22⋊(C47⋊C32) | C2 | semidirect |
| 7. C47×#2158 | C2 | semidirect |
| 84. #2158 | D47 | semidirect |
| 106. C47 | #13713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245474 | 2 |
| #20241589 | 2 |
| #20241587 | 2 |
| #20241565 | 2 |
| C22⋊(C47⋊C32) | 2 |
| C47×#2158 | 2 |
| #13713 | 47 |