Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
988 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 988 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 |
|---|---|---|
| 2. C3×#64079 | C2 | semidirect |
| 3. C32×C4⋊(C3⋊C8) | C2 | semidirect |
| 4. #11722055 | C2 | semidirect |
| 5. #11722052 | C2 | semidirect |
| 24. #64079 | D3 | semidirect |
| 31. C3×C4⋊(C3⋊C8) | D3 | semidirect |
| 102. C4⋊(C3⋊C8) | C3⋊D3 | semidirect |
| 205. C33 | #478 | semidirect |
| 293. C32 | #4847 | semidirect |
| 294. C32 | #5066 | semidirect |
| 331. C3 | #10590308 | semidirect |
| 332. C3 | #10592546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C3×#64079 | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #11722055 | 2 |
| #11722052 | 2 |
| #11722036 | 2 |
| #10592546 | 3 |
| #10590308 | 3 |