Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
562 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 97 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×#88544 | C2 | semidirect |
| 2. C3×#63502 | C2 | semidirect |
| 3. C2×C9×#213 | C2 | semidirect |
| 4. #11721040 | C2 | semidirect |
| 5. C2×#88421 | C2 | semidirect |
| 6. C2×#88417 | C2 | semidirect |
| 7. C3⋊C8×Dic9 | C2 | semidirect |
| 32. #63502 | D3 | semidirect |
| 54. C3⋊(C9⋊C8) | D4 | semidirect |
| 55. C9×C3⋊C8 | D4 | semidirect |
| 99. C3×Dic9 | D8 | semidirect |
| 110. C2×#213 | D9 | semidirect |
| 226. Dic9 | #213 | semidirect |
| 234. C3×C9 | #493 | semidirect |
| 278. C3⋊C8 | #611 | semidirect |
| 341. C9 | #5073 | semidirect |
| 389. C3 | #10588831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88544 | 2 |
| C3×#63502 | 2 |
| C2×C9×#213 | 2 |
| #11721040 | 2 |
| C2×#88421 | 2 |
| C2×#88417 | 2 |
| C3⋊C8×Dic9 | 2 |
| #10591482 | 3 |
| #10588831 | 3 |