Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 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. #17987420 | C3 | semidirect |
| 2. (C3×C19⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 3. #17987310 | C3 | semidirect |
| 4. #17987309 | C3 | semidirect |
| 5. C19×#6856 | C3 | semidirect |
| 34. #6856 | C19⋊C3 | semidirect |
| 81. C19 | #10624665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987420 | 3 |
| (C3×C19⋊C3)⋊H(3,𝔽3) | 3 |
| #17987310 | 3 |
| #17987309 | 3 |
| C19×#6856 | 3 |
| #10624665 | 19 |