Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
428 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #11720912 | C2 | semidirect |
| 4. C9×#815 | C2 | semidirect |
| 5. C3×#63378 | C2 | semidirect |
| 7. #11720277 | C2 | semidirect |
| 14. #88524 | C4 | semidirect |
| 35. #63378 | D3 | semidirect |
| 43. #6226 | C2×C4 | semidirect |
| 49. C3×C8×C9 | C2×C4 | semidirect |
| 104. #815 | D9 | semidirect |
| 142. C8×C9 | C4×D3 | semidirect |
| 212. C3×C9 | #440 | semidirect |
| 246. C3×C8 | C4×D9 | semidirect |
| 304. C9 | #4889 | semidirect |
| 318. C8 | (C3⋊D9)⋊C4 | semidirect |
| 343. C3 | #10588391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| #11720993 | 2 |
| #11720912 | 2 |
| C9×#815 | 2 |
| C3×#63378 | 2 |
| #11720284 | 2 |
| #11720277 | 2 |
| #10590773 | 3 |
| #10588391 | 3 |