Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
620 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 153 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×#88524 | C2 | semidirect |
| 3. #11721712 | C2 | semidirect |
| 4. C4×C4⋊(C3⋊D9) | C2 | semidirect |
| 5. C3×C9×C4⋊C8 | C2 | semidirect |
| 6. #11720543 | C2 | semidirect |
| 7. #11720539 | C2 | semidirect |
| 34. C9×C4⋊C8 | D3 | semidirect |
| 102. C3×C4⋊C8 | D9 | semidirect |
| 202. C4⋊C8 | C3⋊D9 | semidirect |
| 205. C3×C9 | #463 | semidirect |
| 288. C9 | #4844 | semidirect |
| 328. C3 | #10588528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| C2×#88524 | 2 |
| #11721712 | 2 |
| C4×C4⋊(C3⋊D9) | 2 |
| C3×C9×C4⋊C8 | 2 |
| #11720543 | 2 |
| #11720539 | 2 |
| #10592543 | 3 |
| #10588528 | 3 |