Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2380 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 2380 conjugacy classes of subgroups — too many to draw. Only its 635 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×C33×M16 | C2 | semidirect |
| 3. C2×C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. #11722195 | C2 | direct (N × H) |
| 11. #89076 | C4 | semidirect |
| 13. C2×C4⋊(C3⋊(C3⋊D3)) | C4 | semidirect |
| 15. C2×#6308 | C4 | semidirect |
| 17. C33×M16 | C22 | semidirect |
| 20. C4×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 22. C2×C32×M16 | D3 | semidirect |
| 39. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 43. #6308 | C2×C4 | semidirect |
| 57. C32×M16 | C2×D3 | semidirect |
| 74. C2×C3×M16 | C3⋊D3 | semidirect |
| 100. C2×C33 | #104 | semidirect |
| 114. C3×M16 | C2×C3⋊D3 | semidirect |
| 131. C2×M16 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | C2×#104 | semidirect |
| 157. C2×C32 | #825 | semidirect |
| 171. M16 | C2×C3⋊(C3⋊D3) | semidirect |
| 187. C32 | C2×#825 | semidirect |
| 210. C2×C3 | #63652 | semidirect |
| 225. C3 | C2×#63652 | semidirect |
| 229. C2 | #11722195 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89076 | 2 |
| C2×C33×M16 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #11722195 | 2 |
| C2×#63652 | 3 |