Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 240 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. #22582571 | C3 | semidirect |
| 3. C3×#15688505 | C3 | semidirect |
| 4. #22582481 | C3 | semidirect |
| 6. #22582469 | C3 | semidirect |
| 51. C9×C37 | #731 | semidirect |
| 83. C37 | #10624793 | semidirect |
| 116. C9 | #15688515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688515 | 3 |
| #22582571 | 3 |
| C3×#15688505 | 3 |
| #22582481 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582469 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #10624793 | 37 |