Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
254 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C37 | H(3,𝔽3) |
| commutator | C33 | C3×C9×C37 |
| Frattini, cosocle | C34 | C32×C37 |
| prime radical | C34×C37 | C32 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C37 ◁ C34×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C37×C32⋊C9 | C9 | semidirect |
| 34. #10624450 | C37 | direct (N × H) |
| 80. C32⋊C9 | C9×C37 | semidirect |
| 81. C37 | #10624450 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C37×C32⋊C9 | 3 |
| #10624450 | 37 |