Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
952 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 166 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 |
|---|---|---|
| 1. C4×#6308 | C2 | semidirect |
| 3. C2×#88799 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 6. #11722038 | C2 | semidirect |
| 34. C4⋊(C3⋊(C3⋊C8)) | D3 | semidirect |
| 221. C33 | #464 | semidirect |
| 313. C32 | #4845 | semidirect |
| 314. C32 | #5054 | semidirect |
| 353. C3 | #10590378 | semidirect |
| 354. C3 | #10592753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6308 | 2 |
| C32×#875 | 2 |
| C2×#88799 | 2 |
| C2×#88794 | 2 |
| C3×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #11722038 | 2 |
| #11722032 | 2 |
| #10592753 | 3 |
| #10590378 | 3 |