Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2604 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 2604 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×#88855 | C2 | semidirect |
| 4. #11722193 | C2 | direct (N × H) |
| 15. C33×M16 | C22 | semidirect |
| 18. #88855 | C22 | semidirect |
| 21. C2×C32×M16 | D3 | semidirect |
| 51. C32×M16 | C2×D3 | semidirect |
| 69. C2×C3×M16 | C3⋊D3 | semidirect |
| 92. C2×C33 | #100 | semidirect |
| 104. C3×M16 | C2×C3⋊D3 | semidirect |
| 123. C2×M16 | C3⋊(C3⋊D3) | semidirect |
| 125. C33 | C2×#100 | semidirect |
| 145. C2×C32 | #823 | semidirect |
| 159. M16 | C2×C3⋊(C3⋊D3) | semidirect |
| 174. C32 | C2×#823 | semidirect |
| 194. C2×C3 | #63650 | semidirect |
| 209. C3 | C2×#63650 | semidirect |
| 213. C2 | #11722193 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C2×C33×M16 | 2 |
| C2×#88855 | 2 |
| #11722193 | 2 |
| C2×#63650 | 3 |