Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
650 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 73 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. C32×C32⋊(C37⋊C3) | C3 | semidirect |
| 2. C3×#15688518 | C3 | semidirect |
| 3. #22582550 | C3 | semidirect |
| 4. C3×C32⋊#66524 | C3 | semidirect |
| 5. C37×C32⋊H(3,𝔽3) | C3 | semidirect |
| 12. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 13. C32×#66524 | C32 | semidirect |
| 20. C3×H(3,𝔽3)×C37 | C32 | semidirect |
| 41. C32⋊(C37⋊C3) | H(3,𝔽3) | semidirect |
| 57. C32×C37 | #732 | semidirect |
| 71. C32⋊H(3,𝔽3) | C37⋊C3 | semidirect |
| 92. C3×H(3,𝔽3) | C3×C37⋊C3 | semidirect |
| 97. C37 | #10624740 | semidirect |
| 140. C32 | #15688518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C37⋊C3) | 3 |
| C3×#15688518 | 3 |
| #22582550 | 3 |
| C3×C32⋊#66524 | 3 |
| C37×C32⋊H(3,𝔽3) | 3 |
| #10624740 | 37 |