Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
680 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 94 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×#11758608 | C3 | semidirect |
| 2. C3×C32⋊#66524 | C3 | semidirect |
| 3. #22582445 | C3 | direct (N × H) |
| 7. C3×#11758608 | C32 | semidirect |
| 11. C32⋊#66524 | C32 | semidirect |
| 60. C3×C37 | #6857 | semidirect |
| 76. C37 | C3×#6857 | semidirect |
| 115. C3 | #22582445 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758608 | 3 |
| C3×C32⋊#66524 | 3 |
| #22582445 | 3 |
| C32×H(3,𝔽3)×C37 | 3 |
| C3×#6857 | 37 |