Finite Group DatabasebetaFinite Group Databasebeta← (C3×#66526)⋊H(3,𝔽3) #41008453
Order 26973.
842 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 117 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×#66526 | C3 | semidirect |
| 2. C3×C32⋊#66526 | C3 | semidirect |
| 3. C3×C32⋊#66526 | C3 | semidirect |
| 13. C3×C32⋊(C37⋊C3) | C9 | semidirect |
| 14. C3×C32⋊(C37⋊C3) | C9 | semidirect |
| 17. C3×H(3,𝔽3)×C37 | C9 | semidirect |
| 19. C33×C37 | C3×C9 | semidirect |
| 27. C32×C37⋊C3 | C3×C9 | semidirect |
| 36. C3×#66526 | H(3,𝔽3) | semidirect |
| 44. C32×C37 | C32⋊C9 | semidirect |
| 55. C3×C37⋊C3 | C32⋊C9 | semidirect |
| 81. C3×H(3,𝔽3) | #66526 | semidirect |
| 88. C37 | #10624555 | semidirect |
| 101. C33 | C3×#66526 | semidirect |
| 128. C32 | C32⋊#66526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66526 | 3 |
| C3×C32⋊#66526 | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| #10624555 | 37 |