Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
483 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 483 conjugacy classes of subgroups — too many to draw. Only its 118 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. C22×#6855 | C2 | semidirect |
| 2. C2×#92158 | C2 | direct (N × H) |
| 5. C2×#6855 | C22 | semidirect |
| 6. #92158 | C22 | direct (N × H) |
| 12. #6855 | C23 | semidirect |
| 14. C22×C3⋊D9 | C9 | semidirect |
| 35. C22×C3×C9 | D9 | semidirect |
| 36. C22×C3×C9 | C2×C9 | semidirect |
| 37. C2×C3⋊D9 | C2×C9 | semidirect |
| 62. C2×C3×C9 | C2×D9 | semidirect |
| 63. C2×C3×C9 | C22×C9 | semidirect |
| 64. C3⋊D9 | C22×C9 | semidirect |
| 97. C3×C9 | C22×D9 | semidirect |
| 98. C3×C9 | C23×C9 | semidirect |
| 157. C22 | #92158 | direct (N × H) |
| 166. C2 | C2×#92158 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6855 | 2 |
| C2×#92158 | 2 |
| C22×C9×C3⋊D3 | 3 |
| C22×C3×C3⋊D9 | 3 |