Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
488 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 488 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. #22582679 | C3 | semidirect |
| 2. #22582647 | C3 | semidirect |
| 3. #22582644 | C3 | semidirect |
| 4. #22582644 | C3 | semidirect |
| 5. #22582643 | C3 | semidirect |
| 6. #22582639 | C3 | semidirect |
| 7. #22582639 | C3 | semidirect |
| 8. #22582638 | C3 | semidirect |
| 9. #22582637 | C3 | semidirect |
| 10. C3×#15688513 | C3 | semidirect |
| 11. #22582554 | C3 | semidirect |
| 12. #22582550 | C3 | semidirect |
| 13. C3×C37×AΣL(1,𝔽27) | C3 | semidirect |
| 59. 3−1+2×C37 | H(3,𝔽3) | semidirect |
| 92. #11758608 | H(3,𝔽3) | semidirect |
| 97. C3×#66524 | H(3,𝔽3) | semidirect |
| 141. C3×AΣL(1,𝔽27) | C37⋊C3 | semidirect |
| 184. C37 | #10624749 | semidirect |
| 218. 3−1+2 | C32⋊(C37⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582679 | 3 |
| #22582647 | 3 |
| #22582644 | 3 |
| #22582643 | 3 |
| #22582639 | 3 |
| #22582638 | 3 |
| #22582637 | 3 |
| C3×#15688513 | 3 |
| #22582554 | 3 |
| #22582550 | 3 |
| C3×C37×AΣL(1,𝔽27) | 3 |
| #10624749 | 37 |