Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
716 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20243706 | C2 | semidirect |
| 2. C2×#15688857 | C2 | semidirect |
| 3. #20241644 | C2 | semidirect |
| 4. #20241231 | C2 | semidirect |
| 31. C47⋊#95 | D4 | semidirect |
| 246. C47 | #10403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20243706 | 2 |
| C2×#15688857 | 2 |
| #20241644 | 2 |
| #20241231 | 2 |
| C47×#2656 | 2 |
| #10403 | 47 |