Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #20245435 | C2 | semidirect |
| 5. Q8⋊(C47⋊C16) | C2 | semidirect |
| 6. #20241351 | C2 | semidirect |
| 7. C47×#1670 | C2 | semidirect |
| 132. #1670 | D47 | semidirect |
| 157. C47 | #12333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256401 | 2 |
| #20245645 | 2 |
| #20245435 | 2 |
| #20241433 | 2 |
| Q8⋊(C47⋊C16) | 2 |
| #20241351 | 2 |
| C47×#1670 | 2 |
| #12333 | 47 |