Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
820 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #20244221 | C2 | semidirect |
| 2. #20242110 | C2 | semidirect |
| 3. #20242023 | C2 | semidirect |
| 4. #20241896 | C2 | semidirect |
| 6. #15689180 | C22 | semidirect |
| 7. #15689147 | C22 | semidirect |
| 9. #15688969 | C22 | semidirect |
| 16. C47×#555 | C4 | semidirect |
| 18. D42×C47 | C4 | semidirect |
| 162. #555 | Dic47 | semidirect |
| 164. D42 | Dic47 | semidirect |
| 177. C47 | #8491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244221 | 2 |
| #20242110 | 2 |
| #20242023 | 2 |
| #20241896 | 2 |
| C47×#3549 | 2 |
| #8491 | 47 |