Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1140 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 212 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 |
|---|---|---|
| 2. C3×#64078 | C2 | semidirect |
| 3. C32×C4×C3⋊C8 | C2 | semidirect |
| 4. #11722036 | C2 | semidirect |
| 18. #64078 | D3 | semidirect |
| 22. C3×C4×C3⋊C8 | D3 | semidirect |
| 72. C4×C3⋊C8 | C3⋊D3 | semidirect |
| 152. C33 | #486 | semidirect |
| 224. C32 | #4694 | semidirect |
| 225. C32 | #5088 | semidirect |
| 257. C3 | #10590281 | semidirect |
| 258. C3 | #10592393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723915 | 2 |
| C3×#64078 | 2 |
| C32×C4×C3⋊C8 | 2 |
| #11722036 | 2 |
| #10592393 | 3 |
| #10590281 | 3 |