Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
644 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 76 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×C9×C37⋊C3 | C3 | semidirect |
| 2. C3×#15688519 | C3 | semidirect |
| 3. C3×#15688518 | C3 | semidirect |
| 4. (C3×C37⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 5. C3×C37×#732 | C3 | semidirect |
| 29. C3×C9×C37 | H(3,𝔽3) | semidirect |
| 36. C3×#66524 | H(3,𝔽3) | semidirect |
| 51. C3×C37⋊C3 | #732 | semidirect |
| 57. C3×#732 | C37⋊C3 | semidirect |
| 78. C37 | #10624732 | semidirect |
| 98. C3×C9 | C32⋊(C37⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C37⋊C3 | 3 |
| C3×#15688519 | 3 |
| C3×#15688518 | 3 |
| (C3×C37⋊C3)⋊H(3,𝔽3) | 3 |
| C3×C37×#732 | 3 |
| #10624732 | 37 |