Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1064 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 271 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. #737×C37⋊C3 | C3 | semidirect |
| 2. C32×C9×C37⋊C3 | C3 | semidirect |
| 3. #22582634 | C3 | semidirect |
| 4. #22582633 | C3 | semidirect |
| 5. #22582632 | C3 | semidirect |
| 6. #22582631 | C3 | semidirect |
| 7. #22582630 | C3 | semidirect |
| 8. #22582629 | C3 | semidirect |
| 9. #733×C37⋊C3 | C3 | semidirect |
| 10. #732×C37⋊C3 | C3 | semidirect |
| 11. #731×C37⋊C3 | C3 | semidirect |
| 12. AΣL(1,𝔽27)×C37⋊C3 | C3 | semidirect |
| 13. C37×#6908 | C3 | semidirect |
| 16. #15688532 | C32 | semidirect |
| 18. #15688531 | C32 | semidirect |
| 19. #15688530 | C32 | semidirect |
| 23. C32×#66524 | C32 | semidirect |
| 32. C3×C9×C37⋊C3 | C32 | semidirect |
| 33. C3×C9×C37⋊C3 | C32 | semidirect |
| 34. C3×C9×C37⋊C3 | C32 | semidirect |
| 35. #15688521 | C32 | semidirect |
| 36. #15688520 | C32 | semidirect |
| 37. #15688519 | C32 | semidirect |
| 38. #15688518 | C32 | semidirect |
| 39. #15688517 | C32 | semidirect |
| 40. #15688516 | C32 | semidirect |
| 41. #15688515 | C32 | semidirect |
| 42. #15688514 | C32 | semidirect |
| 43. #15688513 | C32 | semidirect |
| 44. #15688512 | C32 | semidirect |
| 45. C37×#737 | C32 | semidirect |
| 46. C32×C9×C37 | C32 | semidirect |
| 47. C37×#733 | C32 | semidirect |
| 48. C37×#732 | C32 | semidirect |
| 49. C37×#731 | C32 | semidirect |
| 50. C37×AΣL(1,𝔽27) | C32 | semidirect |
| 132. #6908 | C37⋊C3 | direct (N × H) |
| 144. C37⋊C3 | #6908 | direct (N × H) |
| 151. #737 | C3×C37⋊C3 | semidirect |
| 167. C32×C9 | C3×C37⋊C3 | semidirect |
| 170. #733 | C3×C37⋊C3 | semidirect |
| 173. #732 | C3×C37⋊C3 | semidirect |
| 177. #731 | C3×C37⋊C3 | semidirect |
| 181. AΣL(1,𝔽27) | C3×C37⋊C3 | semidirect |
| 182. C37 | C3×#6908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #737×C37⋊C3 | 3 |
| C32×C9×C37⋊C3 | 3 |
| #22582634 | 3 |
| #22582633 | 3 |
| #22582632 | 3 |
| #22582631 | 3 |
| #22582630 | 3 |
| #22582629 | 3 |
| #733×C37⋊C3 | 3 |
| #732×C37⋊C3 | 3 |
| #731×C37⋊C3 | 3 |
| AΣL(1,𝔽27)×C37⋊C3 | 3 |
| C37×#6908 | 3 |
| C3×#6908 | 37 |