Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2186 conjugacy classes of subgroups; only the 683 normal subgroups are shown.
This group has 2186 conjugacy classes of subgroups — too many to draw. Only its 683 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. #20251777 | C2 | direct (N × H) |
| 3. C2×#15689007 | C2 | semidirect |
| 4. C2×C43×C47 | C2 | semidirect |
| 8. #15689007 | C22 | semidirect |
| 11. C43×C47 | C22 | semidirect |
| 54. C2×C43 | D47 | semidirect |
| 55. C2×C47 | #2865 | semidirect |
| 64. C43 | C2×D47 | semidirect |
| 65. C47 | C2×#2865 | semidirect |
| 105. C2 | #20251777 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251777 | 2 |
| C2×#15689014 | 2 |
| C2×#15689007 | 2 |
| C2×C43×C47 | 2 |
| C2×#2865 | 47 |