Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
328 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 58 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×C9×#100 | C2 | semidirect |
| 3. C3×#63393 | C2 | semidirect |
| 5. #10588153 | C3 | direct (N × H) |
| 6. C23×C3×D9 | C4 | semidirect |
| 11. C3×#3676 | C4 | semidirect |
| 18. C9×#100 | C2×C3 | semidirect |
| 19. #63393 | C2×C3 | semidirect |
| 36. C23×D9 | C3×C4 | semidirect |
| 47. #3676 | C3×C4 | semidirect |
| 65. C3×#100 | D9 | semidirect |
| 151. #100 | C3×D9 | semidirect |
| 153. C3×C9 | AΣL(1,𝔽16) | semidirect |
| 236. C9 | C3×AΣL(1,𝔽16) | semidirect |
| 276. C3 | #10588153 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63499 | 2 |
| C3×C9×#100 | 2 |
| C3×#63393 | 2 |
| C3×#4475 | 3 |
| #10588153 | 3 |