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. #22582647 | C3 | semidirect |
| 3. #22582638 | C3 | semidirect |
| 4. #22582637 | C3 | semidirect |
| 5. C3×#15688513 | C3 | semidirect |
| 6. #22582550 | C3 | semidirect |
| 7. C37×C32⋊H(3,𝔽3) | C3 | semidirect |
| 8. C3×#11758608 | C32 | semidirect |
| 13. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 20. C34×C37 | C32 | semidirect |
| 23. C3×H(3,𝔽3)×C37 | C32 | semidirect |
| 29. C33×C37 | H(3,𝔽3) | semidirect |
| 34. C32×C37⋊C3 | H(3,𝔽3) | semidirect |
| 48. C32⋊(C37⋊C3) | H(3,𝔽3) | semidirect |
| 82. C32⋊H(3,𝔽3) | C37⋊C3 | semidirect |
| 93. C34 | C3×C37⋊C3 | semidirect |
| 104. C3×H(3,𝔽3) | C3×C37⋊C3 | semidirect |
| 109. C37 | UT(4,𝔽3) | semidirect |
| 119. C33 | 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 |
| #22582647 | 3 |
| #22582638 | 3 |
| #22582637 | 3 |
| C3×#15688513 | 3 |
| #22582550 | 3 |
| C37×C32⋊H(3,𝔽3) | 3 |
| UT(4,𝔽3) | 37 |