Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
328 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 72 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)×#66526 | C3 | semidirect |
| 2. C3×C9×#66526 | C3 | semidirect |
| 3. H(3,𝔽3)⋊#66526 | C3 | semidirect |
| 4. #22582693 | C3 | semidirect |
| 15. #15688519 | C9 | semidirect |
| 16. #15688518 | C9 | semidirect |
| 17. C37×#732 | C9 | semidirect |
| 27. H(3,𝔽3)×C37 | C3×C9 | semidirect |
| 28. C3×C9×C37 | C3×C9 | semidirect |
| 30. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 31. C3×#66524 | C3×C9 | semidirect |
| 47. #66526 | #732 | direct (N × H) |
| 69. #732 | #66526 | direct (N × H) |
| 74. C37 | C9×#732 | semidirect |
| 79. H(3,𝔽3) | C3×#66526 | semidirect |
| 90. C3×C9 | C3×#66526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#66526 | 3 |
| C3×C9×#66526 | 3 |
| H(3,𝔽3)⋊#66526 | 3 |
| #22582693 | 3 |
| #732×C37⋊C3 | 3 |
| C9×#732 | 37 |