Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
565 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 565 conjugacy classes of subgroups — too many to draw. Only its 83 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×C4×C9×A4 | C2 | semidirect |
| 3. C2×C9⋊SL(2,ℤ/4) | C2 | semidirect |
| 10. C2×C9⋊S4 | C4 | semidirect |
| 18. C23×C4×C9 | D3 | semidirect |
| 20. C2×C4×C22⋊C9 | D3 | semidirect |
| 74. C9×A4 | C22⋊C4 | semidirect |
| 80. C2×C4×A4 | D9 | semidirect |
| 119. C2×C4×C9 | S4 | semidirect |
| 184. C22×C9 | (C2×D3)⋊C4 | semidirect |
| 196. C22⋊C9 | (C2×D3)⋊C4 | semidirect |
| 205. C23×C4 | C3⋊D9 | semidirect |
| 311. A4 | (C2×D9)⋊C4 | semidirect |
| 321. C9 | (C2×S4)⋊C4 | semidirect |
| 354. C2×C4 | C9⋊S4 | semidirect |
| 384. C22 | #88536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9⋊S4 | 2 |
| C2×C4×C9×A4 | 2 |
| C2×C9⋊SL(2,ℤ/4) | 2 |
| #10593647 | 3 |
| (C2×(C22⋊C9)⋊C2)⋊C4 | 3 |
| #10588893 | 3 |
| #88536 | 4 |