Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
464 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 144 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×#10587020 | C3 | semidirect |
| 2. #17987557 | C3 | direct (N × H) |
| 5. C3×#10587020 | C32 | semidirect |
| 19. C32×C19⋊C3 | C27 | semidirect |
| 45. C3×C19⋊C3 | C3×C27 | semidirect |
| 61. C3×C19 | C32⋊C27 | semidirect |
| 85. C19 | C3×C32⋊C27 | semidirect |
| 102. C3 | #17987557 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587020 | 3 |
| #17987557 | 3 |
| C32×C9×C19⋊C3 | 3 |
| C3×C32⋊C27 | 19 |