Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
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. #17987584 | C3 | semidirect |
| 2. #17987583 | C3 | semidirect |
| 3. #17987582 | C3 | semidirect |
| 4. (C19⋊C3)⋊C81 | C3 | semidirect |
| 6. #13095335 | C32 | semidirect |
| 72. C19⋊C3 | C81⋊C3 | semidirect |
| 91. C19 | C3×C81⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987584 | 3 |
| #17987583 | 3 |
| #17987582 | 3 |
| (C19⋊C3)⋊C81 | 3 |
| C3×C27×C19⋊C3 | 3 |
| C3×C81⋊C3 | 19 |