Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
230 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 8. #10593560 | C3 | direct (N × H) |
| 127. C33 | #479 | semidirect |
| 183. C32 | C3×#479 | semidirect |
| 215. C3 | #10593560 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×#157 | 2 |
| C3×#64243 | 2 |
| C3×#63784 | 2 |
| C3×#63746 | 2 |
| C3×#63745 | 2 |
| C3×#63744 | 2 |
| #10593560 | 3 |
| C3×#479 | 9 |