Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1004 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 174 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×#64153 | C2 | semidirect |
| 3. C3×#64118 | C2 | semidirect |
| 4. C33×#101 | C2 | semidirect |
| 5. C3×#63652 | C2 | semidirect |
| 6. #10592451 | C3 | direct (N × H) |
| 21. #64153 | C2×C3 | semidirect |
| 22. #64118 | C2×C3 | semidirect |
| 26. C32×#101 | D3 | semidirect |
| 27. C32×#101 | C2×C3 | semidirect |
| 28. #63652 | C2×C3 | semidirect |
| 85. C3×#101 | C3×D3 | semidirect |
| 86. C3×#101 | C3⋊D3 | semidirect |
| 169. #101 | C3×C3⋊D3 | semidirect |
| 170. C33 | #456 | semidirect |
| 240. C32 | #4752 | semidirect |
| 241. C32 | C3×#456 | semidirect |
| 272. C3 | C3×#4752 | semidirect |
| 273. C3 | #10592451 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64364 | 2 |
| C3×#64153 | 2 |
| C3×#64118 | 2 |
| C33×#101 | 2 |
| C3×#63652 | 2 |
| #10592451 | 3 |
| C3×#4752 | 3 |