Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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×C13 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C13 |
| prime radical | C13×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C13 ◁ C34×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#6891 | C3 | semidirect |
| 2. C13×#6891 | C3 | semidirect |
| 4. C13×#6859 | C3 | semidirect |
| 16. #10624667 | C13 | direct (N × H) |
| 31. #6891 | C3×C13 | semidirect |
| 32. #6891 | C3×C13 | semidirect |
| 34. #6859 | C3×C13 | semidirect |
| 84. C13 | #10624667 | direct (N × H) |