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. #22582638 | C3 | semidirect |
| 6. C3×#15688514 | C3 | semidirect |
| 7. (C3×C37⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 8. (C3×C37⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 9. C37×#6909 | C3 | semidirect |
| 10. C33×C37⋊C3 | C32 | semidirect |
| 11. C3×#11758608 | C32 | semidirect |
| 17. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 18. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 26. C3×3−1+2×C37 | C32 | semidirect |
| 28. C3×H(3,𝔽3)×C37 | C32 | semidirect |
| 31. C33×C37 | H(3,𝔽3) | semidirect |
| 41. C32×C37⋊C3 | H(3,𝔽3) | semidirect |
| 62. C32⋊(C37⋊C3) | H(3,𝔽3) | semidirect |
| 98. #6909 | C37⋊C3 | semidirect |
| 115. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 126. C3×H(3,𝔽3) | C3×C37⋊C3 | semidirect |
| 133. C37 | UT(4,𝔽3) | semidirect |
| 144. 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 |
| #22582648 | 3 |
| #22582647 | 3 |
| #22582639 | 3 |
| #22582638 | 3 |
| C3×#15688514 | 3 |
| (C3×C37⋊C3)⋊H(3,𝔽3) | 3 |
| C37×#6909 | 3 |
| UT(4,𝔽3) | 37 |