Finite Group DatabasebetaFinite Group Databasebeta← (C37⋊C3)⋊(C32⋊C27) #41008478
Order 26973.
464 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 129 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×(C37⋊C3)⋊C27 | C3 | semidirect |
| 2. #22582690 | C3 | semidirect |
| 3. C32⋊#11758603 | C3 | semidirect |
| 6. C3×#11758603 | C32 | semidirect |
| 21. C32×C37⋊C3 | C27 | semidirect |
| 45. C32×C37 | C3×C27 | semidirect |
| 52. C3×C37⋊C3 | C3×C27 | semidirect |
| 70. C37⋊C3 | C32⋊C27 | semidirect |
| 84. C37 | C3×C32⋊C27 | semidirect |
| 118. C32 | (C37⋊C3)⋊C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×(C37⋊C3)⋊C27 | 3 |
| #22582690 | 3 |
| C32⋊#11758603 | 3 |
| C32×C9×C37⋊C3 | 3 |
| C3×C32⋊C27 | 37 |