Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 89 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. C3×#63455 | C2 | semidirect |
| 2. #11721040 | C2 | semidirect |
| 3. C2×#88421 | C2 | semidirect |
| 4. C2×#88417 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 6. C9×#809 | C2 | semidirect |
| 7. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 33. #63455 | D3 | semidirect |
| 50. C3×D36 | D4 | semidirect |
| 101. C3×Dic9 | D8 | semidirect |
| 115. #809 | D9 | semidirect |
| 154. D36 | D12 | semidirect |
| 231. Dic9 | #213 | semidirect |
| 239. C3×C9 | #459 | semidirect |
| 350. C9 | #5015 | semidirect |
| 401. C3 | #10588466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63455 | 2 |
| #11721040 | 2 |
| C2×#88421 | 2 |
| C2×#88417 | 2 |
| #11720528 | 2 |
| C9×#809 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #10590547 | 3 |
| #10588466 | 3 |