Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 102 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. C3×2−1+4⋊C9 | C2 | semidirect |
| 2. C3×#63700 | C2 | semidirect |
| 3. C3×#131⋊C9 | C2 | semidirect |
| 5. #577⋊C9 | C3 | direct (N × H) |
| 17. 2−1+4⋊C9 | C2×C3 | semidirect |
| 18. #63700 | C2×C3 | semidirect |
| 19. #131⋊C9 | C2×C3 | semidirect |
| 24. C3×#577 | C9 | semidirect |
| 51. C3×H(5,𝔽2) | C2×C9 | semidirect |
| 61. C3×#131 | C2×C9 | semidirect |
| 84. #577 | C3×C9 | semidirect |
| 131. H(5,𝔽2) | C2×C3×C9 | semidirect |
| 136. #131 | C2×C3×C9 | semidirect |
| 245. C3 | #577⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×2−1+4⋊C9 | 2 |
| C3×#63700 | 2 |
| C3×#131⋊C9 | 2 |
| C32×#577 | 3 |
| #577⋊C9 | 3 |
| C3×C9×SD16 | 4 |