Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
572 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 166 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 |
|---|---|---|
| 4. 3−1+2⋊#66524 | C3 | direct (N × H) |
| 19. C3×3−1+2×C37 | C9 | semidirect |
| 32. 3−1+2×C37 | C3×C9 | semidirect |
| 72. C3×C37 | 3−1+2⋊C9 | semidirect |
| 80. C3×3−1+2 | #66524 | semidirect |
| 93. C37 | C3×3−1+2⋊C9 | semidirect |
| 104. 3−1+2 | C3×#66524 | semidirect |
| 138. C3 | 3−1+2⋊#66524 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66524 | 3 |
| C3×C32⋊#66524 | 3 |
| 3−1+2⋊#66524 | 3 |
| C32×3−1+2×C37 | 3 |
| C3×3−1+2⋊C9 | 37 |