Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
438 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 130 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. C3×#63455 | C2 | semidirect |
| 3. C3×C9×#107 | C2 | semidirect |
| 4. C3×C8×Dic9 | C2 | semidirect |
| 5. C3×#63369 | C2 | semidirect |
| 7. #10588552 | C3 | direct (N × H) |
| 15. C3×D72 | C4 | semidirect |
| 22. #63455 | C2×C3 | semidirect |
| 24. C9×#107 | C2×C3 | semidirect |
| 25. C8×Dic9 | C2×C3 | semidirect |
| 26. #63369 | C2×C3 | semidirect |
| 33. C3×D36 | C2×C4 | semidirect |
| 35. C3×C8×C9 | C2×C4 | semidirect |
| 56. D72 | C3×C4 | semidirect |
| 65. C3×Dic9 | D8 | semidirect |
| 71. C3×#107 | D9 | semidirect |
| 95. D36 | C2×C3×C4 | semidirect |
| 98. C8×C9 | C2×C3×C4 | semidirect |
| 144. Dic9 | C3×D8 | semidirect |
| 147. #107 | C3×D9 | semidirect |
| 150. C3×C9 | C4×D8 | semidirect |
| 171. C3×C8 | C4×D9 | semidirect |
| 217. C9 | C3×C4×D8 | semidirect |
| 227. C8 | C3×C4×D9 | semidirect |
| 249. C3 | #10588552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D72 | 2 |
| C3×#63455 | 2 |
| C3×C9×#107 | 2 |
| C3×C8×Dic9 | 2 |
| C3×#63369 | 2 |
| C3×#4872 | 3 |
| #10588552 | 3 |