Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
266 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 68 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. C2×C3⋊#3771 | C2 | semidirect |
| 3. C2×C3×#3771 | C2 | semidirect |
| 4. #11724094 | C2 | direct (N × H) |
| 11. C3⋊#3771 | C22 | semidirect |
| 12. C3×#3771 | C22 | semidirect |
| 15. C2×#3771 | D3 | semidirect |
| 33. #3771 | C2×D3 | semidirect |
| 59. C2×C33 | M32 | semidirect |
| 89. C33 | C2×M32 | semidirect |
| 108. C2×C32 | #798 | semidirect |
| 137. C32 | C2×#798 | semidirect |
| 150. C2×C3 | #64214 | semidirect |
| 163. C3 | C2×#64214 | semidirect |
| 165. C2 | #11724094 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88924 | 2 |
| C2×C3⋊#3771 | 2 |
| C2×C3×#3771 | 2 |
| #11724094 | 2 |
| C2×#64214 | 3 |
| C2×#798 | 9 |