Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
876 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 220 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 |
|---|---|---|
| 3. Dic6×C3⋊Dic3 | C2 | semidirect |
| 4. #11722187 | C2 | semidirect |
| 5. C3×C8×C3⋊Dic3 | C2 | semidirect |
| 6. #11722038 | C2 | semidirect |
| 18. C32×#204 | C4 | semidirect |
| 33. C8×C3⋊Dic3 | D3 | semidirect |
| 47. C32×Dic6 | C2×C4 | semidirect |
| 49. C33×C8 | C2×C4 | semidirect |
| 76. C3×#204 | Dic3 | semidirect |
| 89. C3×C3⋊Dic3 | SD16 | semidirect |
| 131. C3×Dic6 | C2×Dic3 | semidirect |
| 134. C32×C8 | C4×D3 | semidirect |
| 135. C32×C8 | C2×Dic3 | semidirect |
| 169. #204 | C3⋊Dic3 | direct (N × H) |
| 193. C3⋊Dic3 | #204 | direct (N × H) |
| 204. C33 | C4×SD16 | semidirect |
| 231. Dic6 | C2×C3⋊Dic3 | semidirect |
| 234. C3×C8 | D3×Dic3 | semidirect |
| 235. C3×C8 | C2×C3⋊Dic3 | semidirect |
| 288. C32 | C4×#204 | semidirect |
| 289. C32 | Dic3×SD16 | semidirect |
| 303. C8 | D3×C3⋊Dic3 | semidirect |
| 327. C3 | Dic3×#204 | semidirect |
| 328. C3 | SD16×C3⋊Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#204 | 2 |
| D12×C3⋊Dic3 | 2 |
| Dic6×C3⋊Dic3 | 2 |
| #11722187 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| #11722038 | 2 |
| #11722032 | 2 |
| SD16×C3⋊Dic3 | 3 |
| Dic3×#204 | 3 |