Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2212 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 2212 conjugacy classes of subgroups — too many to draw. Only its 579 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. C33×#117 | C2 | semidirect |
| 3. #11723967 | C2 | semidirect |
| 4. #11722176 | C2 | semidirect |
| 12. C2×C4⋊(C3⋊(C3⋊D3)) | C4 | semidirect |
| 13. C2×C4×C3⋊(C3⋊D3) | C4 | semidirect |
| 14. C2×#6308 | C4 | semidirect |
| 22. C32×#117 | D3 | semidirect |
| 74. C3×#117 | C3⋊D3 | semidirect |
| 132. #117 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | #410 | semidirect |
| 187. C32 | #5006 | semidirect |
| 225. C3 | #10592705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89076 | 2 |
| C33×#117 | 2 |
| #11723967 | 2 |
| #11722176 | 2 |
| #10592705 | 3 |