Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
560 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 61 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. C37⋊H(5,𝔽3) | C3 | semidirect |
| 2. #22582648 | C3 | semidirect |
| 3. #22582647 | C3 | semidirect |
| 4. #22582639 | C3 | semidirect |
| 5. C3×#15688513 | C3 | semidirect |
| 6. #22582550 | C3 | semidirect |
| 7. C3×C37×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C3×#11758608 | C32 | semidirect |
| 13. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 20. C34×C37 | C32 | semidirect |
| 21. C3×3−1+2×C37 | C32 | semidirect |
| 33. C32×C37⋊C3 | H(3,𝔽3) | semidirect |
| 37. H(3,𝔽3)×C37 | H(3,𝔽3) | semidirect |
| 48. C32⋊(C37⋊C3) | H(3,𝔽3) | semidirect |
| 78. C3×AΣL(1,𝔽27) | C37⋊C3 | semidirect |
| 89. C34 | C3×C37⋊C3 | semidirect |
| 91. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 105. C37 | UT(4,𝔽3) | semidirect |
| 131. H(3,𝔽3) | C32⋊(C37⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37⋊H(5,𝔽3) | 3 |
| #22582648 | 3 |
| #22582647 | 3 |
| #22582639 | 3 |
| C3×#15688513 | 3 |
| #22582550 | 3 |
| C3×C37×AΣL(1,𝔽27) | 3 |
| UT(4,𝔽3) | 37 |