Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
655 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 655 conjugacy classes of subgroups — too many to draw. Only its 107 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×C9⋊SL(2,ℤ/4) | C2 | semidirect |
| 7. C22×C9×A4 | C4 | semidirect |
| 36. C24×C9 | Dic3 | semidirect |
| 39. C22×C22⋊C9 | Dic3 | semidirect |
| 55. C9×A4 | C22⋊C4 | semidirect |
| 111. C22×A4 | Dic9 | semidirect |
| 147. C22×C9 | #217 | semidirect |
| 148. C22×C9 | SL(2,ℤ/4) | semidirect |
| 150. C22⋊C9 | #217 | semidirect |
| 208. C24 | C3⋊Dic9 | semidirect |
| 240. A4 | #3676 | semidirect |
| 246. C9 | #5432 | semidirect |
| 298. C22 | #88551 | semidirect |
| 299. C22 | C9⋊SL(2,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C9×A4 | 2 |
| C2×C9⋊SL(2,ℤ/4) | 2 |
| #10593666 | 3 |
| #10589534 | 3 |
| #10588927 | 3 |
| #88551 | 4 |