Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
5588 conjugacy classes of subgroups; only the 2881 normal subgroups are shown.
This group has 5588 conjugacy classes of subgroups — too many to draw. Only its 2881 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. #22582680 | C3 | semidirect |
| 2. #22582679 | C3 | semidirect |
| 3. #22582678 | C3 | semidirect |
| 4. #22582677 | C3 | semidirect |
| 5. #737×C37⋊C3 | C3 | semidirect |
| 6. C3×3−1+2×C37⋊C3 | C3 | semidirect |
| 8. C37×3−1+4 | C3 | semidirect |
| 10. #15688532 | C32 | semidirect |
| 11. #15688531 | C32 | semidirect |
| 12. #15688530 | C32 | semidirect |
| 13. C3×#11758608 | C32 | semidirect |
| 14. C3×#11758605 | C32 | semidirect |
| 15. C3×#11758606 | C32 | semidirect |
| 17. 3−1+2×C37⋊C3 | C32 | semidirect |
| 18. 3−1+2×C37⋊C3 | C32 | semidirect |
| 19. 3−1+2×C37⋊C3 | C32 | semidirect |
| 20. 3−1+2×C37⋊C3 | C32 | semidirect |
| 25. C3×C9×C37⋊C3 | C32 | semidirect |
| 26. C37×#737 | C32 | semidirect |
| 27. C3×3−1+2×C37 | C32 | semidirect |
| 37. 3−1+2×C37 | C33 | semidirect |
| 39. C3×C9×C37 | C33 | semidirect |
| 42. #11758608 | C33 | semidirect |
| 43. C3×#66524 | C33 | semidirect |
| 45. #11758606 | C33 | semidirect |
| 47. #11758605 | C33 | semidirect |
| 49. C9×C37⋊C3 | C33 | semidirect |
| 69. 3−1+4 | C37⋊C3 | direct (N × H) |
| 79. C37⋊C3 | 3−1+4 | direct (N × H) |
| 84. #737 | C3×C37⋊C3 | semidirect |
| 93. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 100. C37 | C3×3−1+4 | semidirect |
| 115. 3−1+2 | C32×C37⋊C3 | semidirect |
| 121. C3×C9 | C32×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582680 | 3 |
| #22582679 | 3 |
| #22582678 | 3 |
| #22582677 | 3 |
| #737×C37⋊C3 | 3 |
| C3×3−1+2×C37⋊C3 | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| C37×3−1+4 | 3 |
| C3×3−1+4 | 37 |