Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11720910 | C2 | semidirect |
| 4. C8×C3⋊Dic9 | C2 | semidirect |
| 6. C3×#63376 | C2 | semidirect |
| 7. #11720265 | C2 | semidirect |
| 21. #88423 | C4 | semidirect |
| 33. #63376 | D3 | semidirect |
| 47. C3×Dic18 | C2×C4 | semidirect |
| 50. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 87. C3⋊Dic9 | SD16 | semidirect |
| 134. Dic18 | C4×D3 | semidirect |
| 205. C3×C9 | C4×SD16 | semidirect |
| 291. C9 | #4788 | semidirect |
| 329. C3 | #10588438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721025 | 2 |
| #11720910 | 2 |
| C2×#88423 | 2 |
| C8×C3⋊Dic9 | 2 |
| C9×#821 | 2 |
| C3×#63376 | 2 |
| #11720265 | 2 |
| #10590742 | 3 |
| #10588438 | 3 |