Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
2072 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 2072 conjugacy classes of subgroups — too many to draw. Only its 76 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. C34×C37⋊C3 | C3 | semidirect |
| 2. C3×#15688514 | C3 | semidirect |
| 3. C3×#15688513 | C3 | semidirect |
| 4. C3×#15688512 | C3 | semidirect |
| 5. #22582551 | C3 | semidirect |
| 6. (C3×C37⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 7. C3×C37×AΣL(1,𝔽27) | C3 | semidirect |
| 14. C3×#11758608 | C32 | semidirect |
| 16. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 22. C3×3−1+2×C37 | C32 | semidirect |
| 23. C3×H(3,𝔽3)×C37 | C32 | semidirect |
| 29. C33×C37 | H(3,𝔽3) | semidirect |
| 45. C32×C37⋊C3 | H(3,𝔽3) | semidirect |
| 81. C3×C37⋊C3 | AΣL(1,𝔽27) | semidirect |
| 88. C3×AΣL(1,𝔽27) | C37⋊C3 | semidirect |
| 108. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 111. C3×H(3,𝔽3) | C3×C37⋊C3 | semidirect |
| 117. C37 | #10624730 | semidirect |
| 137. C33 | C32⋊(C37⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C37⋊C3 | 3 |
| C3×#15688514 | 3 |
| C3×#15688513 | 3 |
| C3×#15688512 | 3 |
| #22582551 | 3 |
| (C3×C37⋊C3)⋊H(3,𝔽3) | 3 |
| C3×C37×AΣL(1,𝔽27) | 3 |
| #10624730 | 37 |