Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
156 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 28 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. C3×#15688519 | C3 | semidirect |
| 2. #22582472 | C3 | semidirect |
| 3. #22582441 | C3 | semidirect |
| 4. C3×C37×#732 | C3 | semidirect |
| 50. C3×#732 | C37⋊C3 | semidirect |
| 69. C37 | #10624480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688519 | 3 |
| #22582472 | 3 |
| #22582441 | 3 |
| C3×C37×#732 | 3 |
| #10624480 | 37 |