Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 3. #20244376 | C2 | semidirect |
| 4. #20242070 | C2 | semidirect |
| 6. #20241277 | C2 | semidirect |
| 7. C47×#1309 | C2 | semidirect |
| 186. #1309 | D47 | semidirect |
| 216. C47 | #9353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252876 | 2 |
| #20252514 | 2 |
| #20244376 | 2 |
| #20242070 | 2 |
| #20241825 | 2 |
| #20241277 | 2 |
| C47×#1309 | 2 |
| #9353 | 47 |