Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
268 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 97 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. 3−1+2×#66524 | C3 | semidirect |
| 3. C3×#15688505 | C3 | semidirect |
| 4. 3−1+2⋊#66524 | C3 | semidirect |
| 6. #22582470 | C3 | semidirect |
| 22. C37×#731 | C9 | semidirect |
| 26. 3−1+2×C37 | C3×C9 | semidirect |
| 32. C3×C9×C37 | C3×C9 | semidirect |
| 76. #731 | #66524 | semidirect |
| 85. C37 | #731⋊C9 | semidirect |
| 89. 3−1+2 | C3×#66524 | semidirect |
| 103. C3×C9 | C3×#66524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#66524 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| C3×#15688505 | 3 |
| 3−1+2⋊#66524 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582470 | 3 |
| C3×C37×#731 | 3 |
| #731⋊C9 | 37 |