Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
320 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 90 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×#13095342 | C3 | semidirect |
| 2. C32×#10587020 | C3 | semidirect |
| 3. #17987568 | C3 | direct (N × H) |
| 6. #13095342 | C32 | semidirect |
| 10. C3×#10587020 | C32 | semidirect |
| 73. C3×C19 | #6873 | semidirect |
| 94. C19 | C3×#6873 | semidirect |
| 109. C3 | #17987568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095342 | 3 |
| C32×#10587020 | 3 |
| #17987568 | 3 |
| C3×#13095331 | 3 |
| C3×#6873 | 19 |