Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
476 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 172 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. #11757822 | C2 | direct (N × H) |
| 4. C2×C9⋊(C22⋊C9) | C3 | semidirect |
| 5. C2×C9×C22⋊C9 | C3 | semidirect |
| 11. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 12. C9×C22⋊C9 | C2×C3 | semidirect |
| 15. C23×C3×C9 | C9 | semidirect |
| 34. C22×C3×C9 | C2×C9 | semidirect |
| 58. C2×C3×C9 | C22⋊C9 | semidirect |
| 79. C3×C9 | C2×C22⋊C9 | semidirect |
| 116. C23 | #6887 | semidirect |
| 128. C22 | C2×#6887 | semidirect |
| 134. C2 | #11757822 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757822 | 2 |
| C23×C32×C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×C9⋊(C22⋊C9) | 3 |
| C2×C9×C22⋊C9 | 3 |
| C2×#6887 | 4 |