Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
164 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22582717 | C3 | semidirect |
| 2. #22582716 | C3 | semidirect |
| 3. #22582715 | C3 | semidirect |
| 4. (C37⋊C3)⋊C81 | C3 | semidirect |
| 6. #15688534 | C32 | semidirect |
| 58. C37⋊C3 | C81⋊C3 | semidirect |
| 73. C37 | C3×C81⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582717 | 3 |
| #22582716 | 3 |
| #22582715 | 3 |
| (C37⋊C3)⋊C81 | 3 |
| C3×C27×C37⋊C3 | 3 |
| C3×C81⋊C3 | 37 |