Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
416 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 416 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. C2×#88414 | C2 | semidirect |
| 3. C2×#88413 | C2 | semidirect |
| 4. #11720542 | C2 | semidirect |
| 5. C3×(C2×D9)⋊C8 | C2 | semidirect |
| 6. C8×C9×Dic3 | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 36. (C2×D9)⋊C8 | D3 | semidirect |
| 52. C9×C3⋊C8 | D4 | semidirect |
| 96. C9×Dic3 | M16 | semidirect |
| 111. C8×Dic3 | D9 | semidirect |
| 227. C3×C9 | #436 | semidirect |
| 266. C3⋊C8 | D36 | semidirect |
| 326. Dic3 | #3663 | semidirect |
| 329. C9 | #4729 | semidirect |
| 374. C3 | #10588370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6192 | 2 |
| C2×#88414 | 2 |
| C2×#88413 | 2 |
| #11720542 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| C8×C9×Dic3 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10590730 | 3 |
| #10588370 | 3 |