Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
430 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 87. C3×C9 | #499 | semidirect |
| 118. C9 | #4683 | semidirect |
| 133. C3 | #10588363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721707 | 2 |
| C3×C4×C8×C9 | 2 |
| #11720541 | 2 |
| #11720540 | 2 |
| #10592382 | 3 |
| #10588363 | 3 |