Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
400 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10593295 | C3 | direct (N × H) |
| 43. C3×#157 | Q16 | semidirect |
| 88. #157 | C3×Q16 | semidirect |
| 102. C33 | #494 | semidirect |
| 147. C32 | C3×#494 | semidirect |
| 168. C3 | #10593295 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64228 | 2 |
| C3×#64222 | 2 |
| C3×#63802 | 2 |
| C3×C8×#157 | 2 |
| #10593295 | 3 |
| C3×#494 | 9 |