Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 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. #22582554 | C3 | semidirect |
| 2. C3×C32⋊#66524 | C3 | semidirect |
| 3. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 6. C32×#66524 | C32 | semidirect |
| 11. C32⋊#66524 | C32 | semidirect |
| 31. H(3,𝔽3)×C37 | 3−1+2 | semidirect |
| 82. C37 | #10624778 | semidirect |
| 98. H(3,𝔽3) | #11758608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582554 | 3 |
| C3×C32⋊#66524 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| C32×H(3,𝔽3)×C37 | 3 |
| #10624778 | 37 |