Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #20243005 | C2 | semidirect |
| 5. #20241457 | C2 | semidirect |
| 6. #20241444 | C2 | semidirect |
| 7. C47×#1364 | C2 | semidirect |
| 64. D376 | Q16 | semidirect |
| 109. #1364 | D47 | semidirect |
| 129. C47 | #12445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245526 | 2 |
| #20245522 | 2 |
| #20243005 | 2 |
| #20242182 | 2 |
| #20241457 | 2 |
| #20241444 | 2 |
| C47×#1364 | 2 |
| #12445 | 47 |