Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
448 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 112 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. #11757821 | C2 | direct (N × H) |
| 5. C2×C9⋊(C22⋊C9) | C3 | semidirect |
| 6. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 13. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 14. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 55. C23×C9 | 3−1+2 | semidirect |
| 90. C22×C9 | C2×3−1+2 | semidirect |
| 123. C2×C9 | #1094 | semidirect |
| 143. C9 | C2×#1094 | semidirect |
| 144. C23 | #6894 | semidirect |
| 159. C22 | C2×#6894 | semidirect |
| 166. C2 | #11757821 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757821 | 2 |
| C23×C32×C9 | 3 |
| C2×C3×#1094 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×C9⋊(C22⋊C9) | 3 |
| C2×(C22⋊C9)⋊C9 | 3 |
| C2×#6894 | 4 |