Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
356 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C19 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C19 |
| prime radical | C34×C19 | C32 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C19 ◁ C34×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C19×#6860 | C3 | semidirect |
| 24. #10624612 | C19 | direct (N × H) |
| 48. #6860 | C3×C19 | semidirect |
| 116. C19 | #10624612 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C19×3−1+2 | 3 |
| C19×#6891 | 3 |
| C3×C19×C32⋊C9 | 3 |
| C19×#6860 | 3 |
| #10624612 | 19 |