Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20244216 | C2 | semidirect |
| 3. #20242147 | C2 | semidirect |
| 4. #20241840 | C2 | semidirect |
| 5. C42×C8×C47 | C2 | semidirect |
| 7. #15689528 | C4 | semidirect |
| 8. #15689500 | C4 | semidirect |
| 9. #15689470 | C4 | semidirect |
| 67. C42×C47 | D8 | semidirect |
| 104. C8×C47 | #104 | semidirect |
| 125. C42×C8 | D47 | semidirect |
| 147. C47 | #9844 | semidirect |
| 202. C42 | D376 | semidirect |
| 233. C8 | #13093952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253967 | 2 |
| #20244216 | 2 |
| #20242147 | 2 |
| #20241840 | 2 |
| C42×C8×C47 | 2 |
| #9844 | 47 |