Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
224 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 49 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. #733×C37⋊C3 | C3 | semidirect |
| 2. #732×C37⋊C3 | C3 | semidirect |
| 3. C9⋊C9×C37⋊C3 | C3 | semidirect |
| 4. #22582515 | C3 | semidirect |
| 5. #22582514 | C3 | semidirect |
| 6. #22582513 | C3 | semidirect |
| 7. #22582512 | C3 | semidirect |
| 8. #22582511 | C3 | semidirect |
| 9. C37×#6881 | C3 | semidirect |
| 14. #15688521 | C32 | semidirect |
| 16. #15688519 | C32 | semidirect |
| 17. #15688519 | C32 | semidirect |
| 19. #15688506 | C32 | semidirect |
| 20. #15688505 | C32 | semidirect |
| 22. C37×#733 | C32 | semidirect |
| 23. C37×#732 | C32 | semidirect |
| 24. C37×C9⋊C9 | C32 | semidirect |
| 71. #6881 | C37⋊C3 | direct (N × H) |
| 79. C37⋊C3 | #6881 | direct (N × H) |
| 86. #733 | C3×C37⋊C3 | semidirect |
| 90. #732 | C3×C37⋊C3 | semidirect |
| 94. C9⋊C9 | C3×C37⋊C3 | semidirect |
| 95. C37 | C3×#6881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #733×C37⋊C3 | 3 |
| #732×C37⋊C3 | 3 |
| C9⋊C9×C37⋊C3 | 3 |
| #22582515 | 3 |
| #22582514 | 3 |
| #22582513 | 3 |
| #22582512 | 3 |
| #22582511 | 3 |
| C37×#6881 | 3 |
| C3×#6881 | 37 |