Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
680 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 166 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. C33×#66524 | C3 | semidirect |
| 2. C3×C32⋊#66524 | C3 | semidirect |
| 3. H(3,𝔽3)⋊#66524 | C3 | direct (N × H) |
| 9. C32×#66524 | C32 | semidirect |
| 11. C32⋊#66524 | C32 | semidirect |
| 16. C3×H(3,𝔽3)×C37 | C9 | semidirect |
| 33. H(3,𝔽3)×C37 | C3×C9 | semidirect |
| 72. C3×C37 | H(3,𝔽3)⋊C9 | semidirect |
| 81. C3×H(3,𝔽3) | #66524 | semidirect |
| 90. C37 | C3×H(3,𝔽3)⋊C9 | semidirect |
| 106. H(3,𝔽3) | C3×#66524 | semidirect |
| 140. C3 | H(3,𝔽3)⋊#66524 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66524 | 3 |
| C3×C32⋊#66524 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| C32×H(3,𝔽3)×C37 | 3 |
| C3×H(3,𝔽3)⋊C9 | 37 |