Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
460 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20241712 | C2 | semidirect |
| 3. #20241331 | C2 | semidirect |
| 5. C47×#1461 | C2 | semidirect |
| 26. #13094013 | C8 | semidirect |
| 174. #1461 | D47 | semidirect |
| 200. C47 | #11476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13094013 | 2 |
| #20241712 | 2 |
| #20241331 | 2 |
| #20241319 | 2 |
| C47×#1461 | 2 |
| #11476 | 47 |