Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
494 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 113 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×#88524 | C2 | semidirect |
| 2. C2×C3×#3664 | C2 | semidirect |
| 4. #11720932 | C2 | semidirect |
| 5. C2×#88416 | C2 | semidirect |
| 6. C2×#88415 | C2 | semidirect |
| 7. C8×C9×Dic3 | C2 | semidirect |
| 34. C2×#3664 | D3 | semidirect |
| 53. C3×C8×C9 | D4 | semidirect |
| 54. C9×C3⋊C8 | D4 | semidirect |
| 95. C9×Dic3 | SD16 | semidirect |
| 111. C8×Dic3 | D9 | semidirect |
| 153. C8×C9 | #67 | semidirect |
| 222. C3×C9 | #492 | semidirect |
| 262. C3×C8 | D36 | semidirect |
| 264. C3⋊C8 | D36 | semidirect |
| 314. Dic3 | #3664 | semidirect |
| 317. C9 | #5175 | semidirect |
| 334. C8 | #6192 | semidirect |
| 357. C3 | #10588375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| C2×C3×#3664 | 2 |
| #11721006 | 2 |
| #11720932 | 2 |
| C2×#88416 | 2 |
| C2×#88415 | 2 |
| C8×C9×Dic3 | 2 |
| #10590877 | 3 |
| #10588375 | 3 |