Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
478 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 105 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. #11720992 | C2 | semidirect |
| 3. C9×#818 | C2 | semidirect |
| 4. C3×C8×Dic9 | C2 | semidirect |
| 5. #11720267 | C2 | semidirect |
| 11. #88525 | C4 | semidirect |
| 25. C8×Dic9 | D3 | semidirect |
| 30. C4⋊(C3⋊D9) | C2×C4 | semidirect |
| 35. C3×C8×C9 | C2×C4 | semidirect |
| 66. C3×Dic9 | D8 | semidirect |
| 75. #818 | D9 | semidirect |
| 101. C8×C9 | C4×D3 | semidirect |
| 150. Dic9 | D24 | semidirect |
| 156. C3×C9 | C4×D8 | semidirect |
| 179. C3×C8 | C4×D9 | semidirect |
| 228. C9 | C4×D24 | semidirect |
| 238. C8 | (C3⋊D9)⋊C4 | semidirect |
| 261. C3 | #10588552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| #11720992 | 2 |
| C9×#818 | 2 |
| C3×C8×Dic9 | 2 |
| #11720267 | 2 |
| #10590763 | 3 |
| #10588552 | 3 |