Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
320 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 52 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. #17987421 | C3 | semidirect |
| 2. #17987417 | C3 | semidirect |
| 3. #17987309 | C3 | semidirect |
| 4. C19×C32⋊H(3,𝔽3) | C3 | semidirect |
| 34. C32⋊H(3,𝔽3) | C19⋊C3 | semidirect |
| 89. C19 | #10624665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987421 | 3 |
| #17987417 | 3 |
| #17987309 | 3 |
| C19×C32⋊H(3,𝔽3) | 3 |
| #10624665 | 19 |