Finite Group DatabasebetaFinite Group DatabasebetaOrder 2187.
162 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C9 | #6896 |
| commutator, Frattini, cosocle | C32×C9 | C33 |
| socle | C3 | #10624575 |
| prime radical | C33 | #737 |
| LCS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9 ◁ C32×C9 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624709 | 3 |
| #10624707 | 3 |
| #10624473 | 3 |
| #10624471 | 3 |
| #10624470 | 3 |
| #10624469 | 3 |
| #10624468 | 3 |
| #10624465 | 3 |