Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
544 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 544 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. #20252105 | C2 | semidirect |
| 3. #20244185 | C2 | semidirect |
| 4. #20242038 | C2 | semidirect |
| 5. #20241812 | C2 | semidirect |
| 6. #20241232 | C2 | semidirect |
| 7. C47×#1301 | C2 | semidirect |
| 122. C2×C47⋊C8 | D8 | semidirect |
| 206. #1301 | D47 | semidirect |
| 236. C47 | #9049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253389 | 2 |
| #20252105 | 2 |
| #20244185 | 2 |
| #20242038 | 2 |
| #20241812 | 2 |
| #20241232 | 2 |
| C47×#1301 | 2 |
| #9049 | 47 |