Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
992 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 274 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. C3×#15688532 | C3 | semidirect |
| 2. C32×#11758605 | C3 | semidirect |
| 3. #22582662 | C3 | direct (N × H) |
| 4. C3×#15688521 | C3 | semidirect |
| 5. C3×#15688519 | C3 | semidirect |
| 6. C3×#15688517 | C3 | semidirect |
| 7. C3×#15688514 | C3 | semidirect |
| 8. C3×C37×#733 | C3 | semidirect |
| 11. #15688532 | C32 | semidirect |
| 16. C3×#11758605 | C32 | semidirect |
| 22. #15688521 | C32 | semidirect |
| 23. #15688519 | C32 | semidirect |
| 24. #15688517 | C32 | semidirect |
| 25. #15688514 | C32 | semidirect |
| 28. C37×#733 | C32 | semidirect |
| 76. C3×#733 | C37⋊C3 | semidirect |
| 82. C3×C37 | #6913 | semidirect |
| 102. #733 | C3×C37⋊C3 | semidirect |
| 106. C37 | C3×#6913 | semidirect |
| 153. C3 | #22582662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| C32×#11758605 | 3 |
| #22582662 | 3 |
| C3×#15688521 | 3 |
| C3×#15688519 | 3 |
| C3×#15688517 | 3 |
| C3×#15688514 | 3 |
| C3×C37×#733 | 3 |
| C3×#6913 | 37 |