Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
273 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 45 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. Q8×C9×A4 | C2 | semidirect |
| 3. A4×C9⋊C8 | C2 | semidirect |
| 5. C22×#3675 | C3 | semidirect |
| 13. C22×Q8×C9 | C2×C3 | semidirect |
| 20. C22×C9⋊C8 | C2×C3 | semidirect |
| 47. #3675 | A4 | direct (N × H) |
| 51. C9×A4 | SD16 | semidirect |
| 57. Q8×A4 | D9 | semidirect |
| 80. Q8×C9 | C2×A4 | semidirect |
| 90. C9⋊C8 | C2×A4 | semidirect |
| 122. C22×C9 | C3×SD16 | semidirect |
| 136. C22×Q8 | C3×D9 | semidirect |
| 205. A4 | #3675 | direct (N × H) |
| 216. C9 | A4×SD16 | semidirect |
| 225. Q8 | A4×D9 | semidirect |
| 252. C22 | C3×#3675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9×A4 | 2 |
| A4×D36 | 2 |
| A4×C9⋊C8 | 2 |
| A4×#215 | 3 |
| C22×#3675 | 3 |
| C3×#3675 | 4 |