Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
268 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 2. #22582558 | C3 | semidirect |
| 3. C3×#15688505 | C3 | semidirect |
| 4. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 5. #22582475 | C3 | semidirect |
| 6. #22582471 | C3 | semidirect |
| 7. C9×H(3,𝔽3)×C37 | C3 | semidirect |
| 26. H(3,𝔽3)×C37 | 3−1+2 | semidirect |
| 55. C9×C37 | #732 | semidirect |
| 61. C9×H(3,𝔽3) | C37⋊C3 | semidirect |
| 87. C37 | #10624792 | semidirect |
| 95. H(3,𝔽3) | #11758605 | semidirect |
| 123. C9 | #15688518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688518 | 3 |
| #22582558 | 3 |
| C3×#15688505 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582475 | 3 |
| #22582471 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #10624792 | 37 |