Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1244 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 316 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. C32×#11758606 | C3 | semidirect |
| 3. #22582560 | C3 | semidirect |
| 4. #22582559 | C3 | semidirect |
| 5. #22582552 | C3 | semidirect |
| 6. H(3,𝔽3)×#66524 | C3 | semidirect |
| 7. C9×H(3,𝔽3)×C37 | C3 | semidirect |
| 12. C3×#11758606 | C32 | semidirect |
| 13. C3×#11758606 | C32 | semidirect |
| 16. C32×#66524 | C32 | semidirect |
| 17. C32⋊#66524 | C32 | semidirect |
| 18. #15688502 | C32 | semidirect |
| 20. C32×C9×C37 | C32 | semidirect |
| 21. C37×C32⋊C9 | C32 | semidirect |
| 28. H(3,𝔽3)×C37 | 3−1+2 | semidirect |
| 39. #11758606 | H(3,𝔽3) | direct (N × H) |
| 43. C32×C37 | C3×3−1+2 | semidirect |
| 53. C9×C37 | C3×H(3,𝔽3) | semidirect |
| 55. #66524 | C3×H(3,𝔽3) | semidirect |
| 62. C9×H(3,𝔽3) | C37⋊C3 | semidirect |
| 79. C32×C9 | C3×C37⋊C3 | semidirect |
| 82. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 83. C37 | H(3,𝔽3)×3−1+2 | semidirect |
| 95. H(3,𝔽3) | #11758606 | direct (N × H) |
| 111. C32 | C3×#11758606 | semidirect |
| 116. C9 | H(3,𝔽3)×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758606 | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| #22582560 | 3 |
| #22582559 | 3 |
| #22582552 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| H(3,𝔽3)×3−1+2 | 37 |