Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
276 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 64 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. #22582572 | C3 | semidirect |
| 3. C3×#15688502 | C3 | semidirect |
| 4. #22582478 | C3 | semidirect |
| 5. #22582478 | C3 | semidirect |
| 6. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 7. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 8. #22582467 | C3 | semidirect |
| 9. C9×H(3,𝔽3)×C37 | C3 | semidirect |
| 78. C9×H(3,𝔽3) | C37⋊C3 | semidirect |
| 110. C37 | #10624797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688512 | 3 |
| #22582572 | 3 |
| C3×#15688502 | 3 |
| #22582478 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582467 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #10624797 | 37 |