Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
293 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 293 conjugacy classes of subgroups — too many to draw. Only its 53 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 | C32⋊H(3,𝔽3) |
| commutator, Frattini, prime radical, cosocle | C34 | C33 |
| LCS | G ▷ C34 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32 ◁ C34 ◁ G | |
| LECS | G ▷ C34 ▷ C32 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624886 | 3 |
| #10624826 | 3 |
| #10624822 | 3 |
| #10624807 | 3 |
| #10624776 | 3 |
| #10624775 | 3 |
| #10624617 | 3 |
| #10624616 | 3 |
| #10624615 | 3 |
| #10624614 | 3 |
| #10624605 | 3 |
| #10624600 | 3 |
| #10624570 | 3 |