Finite Group DatabasebetaFinite Group Databasebeta← C2×C9⋊(C22⋊(C22⋊C9)) #72276028
Order 2592.
1438 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 1438 conjugacy classes of subgroups — too many to draw. Only its 148 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. C9⋊(C22⋊(C22⋊C9)) | C2 | direct (N × H) |
| 11. C25×C9 | C9 | semidirect |
| 25. C24×C9 | C2×C9 | semidirect |
| 45. C23×C9 | C22⋊C9 | semidirect |
| 66. C22×C9 | C2×C22⋊C9 | semidirect |
| 68. C25 | C9⋊C9 | semidirect |
| 87. C2×C9 | C22⋊(C22⋊C9) | semidirect |
| 90. C24 | C2×C9⋊C9 | semidirect |
| 103. C9 | C2×C22⋊(C22⋊C9) | semidirect |
| 108. C23 | C9⋊(C22⋊C9) | semidirect |
| 119. C22 | C2×C9⋊(C22⋊C9) | semidirect |
| 124. C2 | C9⋊(C22⋊(C22⋊C9)) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9⋊(C22⋊(C22⋊C9)) | 2 |
| C25×C3×C9 | 3 |
| C2×C3×C22⋊(C22⋊C9) | 3 |
| C2×C9⋊(C22⋊C9) | 4 |