Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
744 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 93 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×C4×C3⋊#157 | C2 | semidirect |
| 3. C2×#88989 | C2 | semidirect |
| 4. #11723110 | C2 | direct (N × H) |
| 7. C2×C33×Q8 | C4 | semidirect |
| 10. C3×#3832 | C4 | semidirect |
| 13. C2×C3×C4⋊(C3⋊D3) | C4 | semidirect |
| 18. C4×C3⋊#157 | C22 | semidirect |
| 20. #88989 | C22 | semidirect |
| 31. C33×Q8 | C2×C4 | semidirect |
| 38. C3×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 50. C2×C32×Q8 | Dic3 | semidirect |
| 53. #3832 | Dic3 | semidirect |
| 56. C2×C4⋊(C3⋊D3) | Dic3 | semidirect |
| 100. C32×Q8 | C2×Dic3 | semidirect |
| 111. C4⋊(C3⋊D3) | C2×Dic3 | semidirect |
| 131. C2×C33 | #104 | semidirect |
| 142. C2×C3×Q8 | #157 | semidirect |
| 192. C33 | C2×#104 | semidirect |
| 202. C3×Q8 | C2×#157 | semidirect |
| 238. C2×C32 | #837 | semidirect |
| 250. C2×Q8 | C3⋊#157 | semidirect |
| 290. C32 | C2×#837 | semidirect |
| 294. Q8 | C2×C3⋊#157 | semidirect |
| 318. C2×C3 | #63785 | semidirect |
| 337. C3 | C2×#63785 | semidirect |
| 341. C2 | #11723110 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3832 | 2 |
| C2×C4×C3⋊#157 | 2 |
| C2×#88989 | 2 |
| #11723110 | 2 |
| C2×#63785 | 3 |
| C2×#837 | 9 |