Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
512 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 87 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. C3×C32⋊#66526 | C3 | semidirect |
| 2. C3×C32⋊#66526 | C3 | semidirect |
| 3. H(3,𝔽3)⋊#66526 | C3 | semidirect |
| 6. C32×#66526 | C32 | semidirect |
| 11. C32⋊#66526 | C32 | semidirect |
| 15. C3×C32⋊(C37⋊C3) | C9 | semidirect |
| 18. H(3,𝔽3)×C37⋊C3 | C9 | semidirect |
| 20. C3×H(3,𝔽3)×C37 | C9 | semidirect |
| 43. H(3,𝔽3)×C37 | C3×C9 | semidirect |
| 47. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 103. C3×H(3,𝔽3) | #66526 | semidirect |
| 111. C37 | #10624698 | semidirect |
| 134. H(3,𝔽3) | C3×#66526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊#66526 | 3 |
| H(3,𝔽3)⋊#66526 | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| #10624698 | 37 |