Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#88420 | C2 | semidirect |
| 3. C2×#88413 | C2 | semidirect |
| 4. C8×C3⋊Dic9 | C2 | semidirect |
| 5. C9×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C3×(C2×D9)⋊C8 | C2 | semidirect |
| 7. #11720273 | C2 | semidirect |
| 34. (C2×D9)⋊C8 | D3 | semidirect |
| 51. C3⋊(C9⋊C8) | D4 | semidirect |
| 95. C3⋊Dic9 | M16 | semidirect |
| 107. (C2×D3)⋊C8 | D9 | semidirect |
| 223. C3×C9 | #436 | semidirect |
| 320. C9 | #4729 | semidirect |
| 364. C3 | #10588411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6194 | 2 |
| C2×#88420 | 2 |
| C2×#88413 | 2 |
| C8×C3⋊Dic9 | 2 |
| C9×(C2×D3)⋊C8 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| #11720273 | 2 |
| #10590734 | 3 |
| #10588411 | 3 |