Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
280 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20245617 | C2 | semidirect |
| 4. #20242986 | C2 | semidirect |
| 6. #20241304 | C2 | semidirect |
| 7. C47×#2252 | C2 | semidirect |
| 67. C16×C47 | SD16 | semidirect |
| 100. #2252 | D47 | semidirect |
| 126. C47 | #12508 | semidirect |
| 172. C16 | #10625336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245644 | 2 |
| #20245617 | 2 |
| #20245613 | 2 |
| #20242986 | 2 |
| #20242981 | 2 |
| #20241304 | 2 |
| C47×#2252 | 2 |
| #12508 | 47 |