Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 107 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. C4×#13093956 | C2 | semidirect |
| 4. #20241243 | C2 | semidirect |
| 5. C47×#1568 | C2 | semidirect |
| 7. #15689253 | C4 | semidirect |
| 8. C8×Dic94 | C4 | semidirect |
| 9. #15689202 | C4 | semidirect |
| 11. C8×D188 | C4 | semidirect |
| 150. #1568 | D47 | semidirect |
| 177. C47 | #8696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252363 | 2 |
| C4×#13093956 | 2 |
| #20241914 | 2 |
| #20241243 | 2 |
| C47×#1568 | 2 |
| #8696 | 47 |