Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
650 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 82 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×#15688518 | C3 | semidirect |
| 2. #22582550 | C3 | semidirect |
| 3. C3×C32⋊#66524 | C3 | semidirect |
| 4. C32×H(3,𝔽3)×C37 | C3 | semidirect |
| 7. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 8. C32×#66524 | C32 | semidirect |
| 30. H(3,𝔽3)×C37 | H(3,𝔽3) | semidirect |
| 49. C32×C37 | #732 | semidirect |
| 56. C32×H(3,𝔽3) | C37⋊C3 | semidirect |
| 80. C37 | #10624740 | semidirect |
| 97. H(3,𝔽3) | C32⋊(C37⋊C3) | semidirect |
| 115. C32 | #15688518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688518 | 3 |
| #22582550 | 3 |
| C3×C32⋊#66524 | 3 |
| C32×H(3,𝔽3)×C37 | 3 |
| #10624740 | 37 |