Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #20241460 | C2 | semidirect |
| 5. #20241446 | C2 | semidirect |
| 6. #20241443 | C2 | semidirect |
| 7. C47×#2254 | C2 | semidirect |
| 64. C16×C47 | SD16 | semidirect |
| 99. #2254 | D47 | semidirect |
| 125. C47 | #12456 | semidirect |
| 168. C16 | #10625336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245221 | 2 |
| #20242784 | 2 |
| #20242774 | 2 |
| #20241460 | 2 |
| #20241446 | 2 |
| #20241443 | 2 |
| C47×#2254 | 2 |
| #12456 | 47 |