Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
500 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C3×3−1+2×C37⋊C3 | C3 | semidirect |
| 2. C3×#15688517 | C3 | semidirect |
| 3. C3×#15688517 | C3 | semidirect |
| 4. C3×#15688516 | C3 | semidirect |
| 5. C3×#15688515 | C3 | semidirect |
| 6. #22582551 | C3 | semidirect |
| 8. C3×#15688502 | C3 | semidirect |
| 9. C3×C37×#731 | C3 | semidirect |
| 52. 3−1+2×C37 | H(3,𝔽3) | semidirect |
| 71. #11758608 | H(3,𝔽3) | semidirect |
| 109. C3×C37⋊C3 | #731 | semidirect |
| 121. C3×#731 | C37⋊C3 | semidirect |
| 164. C37 | #10624745 | semidirect |
| 187. 3−1+2 | C32⋊(C37⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C37⋊C3 | 3 |
| C3×#15688517 | 3 |
| C3×#15688516 | 3 |
| C3×#15688515 | 3 |
| #22582551 | 3 |
| (C3×C37⋊C3)⋊H(3,𝔽3) | 3 |
| C3×#15688502 | 3 |
| C3×C37×#731 | 3 |
| #10624745 | 37 |