Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
338 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 154 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. #10588362 | C3 | direct (N × H) |
| 23. C3×C8×C9 | Q8 | semidirect |
| 65. C8×C9 | C3×Q8 | semidirect |
| 99. C3×C9 | #500 | semidirect |
| 114. C3×C8 | Dic18 | semidirect |
| 146. C9 | C3×#500 | semidirect |
| 152. C8 | C3×Dic18 | semidirect |
| 168. C3 | #10588362 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63431 | 2 |
| C3×C4×C8×C9 | 2 |
| C3×#63378 | 2 |
| C3×#4682 | 3 |
| #10588362 | 3 |