Finite Group DatabasebetaFinite Group Databasebeta← H(3,𝔽3)×(C22⋊C9)⋊C2 #14517972
Order 1944.
283 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 283 conjugacy classes of subgroups — too many to draw. Only its 42 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. H(3,𝔽3)×C22⋊C9 | C2 | semidirect |
| 2. C32×(C22⋊C9)⋊C2 | C3 | semidirect |
| 7. C32×C22⋊C9 | C2×C3 | semidirect |
| 23. C22×H(3,𝔽3) | D9 | semidirect |
| 35. (C22⋊C9)⋊C2 | H(3,𝔽3) | direct (N × H) |
| 47. C22×C32 | C3×D9 | semidirect |
| 56. C22⋊C9 | C2×H(3,𝔽3) | semidirect |
| 59. H(3,𝔽3) | (C22⋊C9)⋊C2 | direct (N × H) |
| 90. C32 | C3×(C22⋊C9)⋊C2 | semidirect |
| 105. C22 | D9×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×C22⋊C9 | 2 |
| C32×(C22⋊C9)⋊C2 | 3 |
| #67×H(3,𝔽3) | 3 |
| D9×H(3,𝔽3) | 4 |