Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
202 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 5. #10593534 | C3 | direct (N × H) |
| 69. C33 | #499 | semidirect |
| 101. C32 | C3×#499 | semidirect |
| 120. C3 | #10593534 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64243 | 2 |
| C3×#63769 | 2 |
| C3×C8×#157 | 2 |
| C3×#63745 | 2 |
| #10593534 | 3 |
| C3×#499 | 9 |