Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
980 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 216 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. #11723499 | C2 | semidirect |
| 3. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. C3×#63645 | C2 | semidirect |
| 5. #11722031 | C2 | semidirect |
| 14. C32×D24 | C4 | semidirect |
| 21. #63645 | D3 | semidirect |
| 33. C32×D12 | C2×C4 | semidirect |
| 35. C33×C8 | C2×C4 | semidirect |
| 56. C3×D24 | Dic3 | semidirect |
| 65. C3⋊(C3⋊Dic3) | D8 | semidirect |
| 95. C3×D12 | C2×Dic3 | semidirect |
| 98. C32×C8 | C4×D3 | semidirect |
| 99. C32×C8 | C2×Dic3 | semidirect |
| 126. D24 | C3⋊Dic3 | semidirect |
| 155. C33 | C4×D8 | semidirect |
| 173. D12 | C2×C3⋊Dic3 | semidirect |
| 176. C3×C8 | D3×Dic3 | semidirect |
| 177. C3×C8 | C2×C3⋊Dic3 | semidirect |
| 224. C32 | #4872 | semidirect |
| 225. C32 | Dic3×D8 | semidirect |
| 235. C8 | D3×C3⋊Dic3 | semidirect |
| 257. C3 | #10590777 | semidirect |
| 258. C3 | D8×C3⋊Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D24 | 2 |
| #11723499 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| C3×#63645 | 2 |
| #11722031 | 2 |
| D8×C3⋊Dic3 | 3 |
| #10590777 | 3 |