Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 85 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×C3×D72 | C2 | semidirect |
| 2. #11721043 | C2 | semidirect |
| 3. #11720998 | C2 | semidirect |
| 4. C2×#88421 | C2 | semidirect |
| 5. #11720537 | C2 | semidirect |
| 6. C9×#821 | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 32. C2×D72 | D3 | semidirect |
| 50. C3×D36 | D4 | semidirect |
| 100. C3⋊Dic9 | D8 | semidirect |
| 112. #821 | D9 | semidirect |
| 152. D36 | #67 | semidirect |
| 236. C3×C9 | #459 | semidirect |
| 343. C9 | #5150 | semidirect |
| 393. C3 | #10588466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D72 | 2 |
| #11721043 | 2 |
| #11720998 | 2 |
| C2×#88421 | 2 |
| #11720537 | 2 |
| C9×#821 | 2 |
| #11720266 | 2 |
| #10590749 | 3 |
| #10588466 | 3 |