Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#88543 | C2 | semidirect |
| 2. C3×D4×Dic9 | C2 | semidirect |
| 4. #11720964 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 6. #11720277 | C2 | semidirect |
| 7. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 32. D4×Dic9 | D3 | semidirect |
| 230. C3×C9 | #463 | semidirect |
| 333. C9 | #5016 | semidirect |
| 378. C3 | #10588833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88543 | 2 |
| C3×D4×Dic9 | 2 |
| C2×C9×#213 | 2 |
| #11720964 | 2 |
| #11720294 | 2 |
| #11720277 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #10591468 | 3 |
| #10588833 | 3 |