Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
542 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 53 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×#89092 | C2 | semidirect |
| 3. C3×C22⋊PSU(3,𝔽2) | C2 | semidirect |
| 4. #11724243 | C2 | semidirect |
| 5. #11724101 | C2 | semidirect |
| 9. C2×C3×PSU(3,𝔽2) | C22 | semidirect |
| 13. C2×C3⋊AGL(1,𝔽9) | C22 | semidirect |
| 17. C3×#3777 | C22 | semidirect |
| 20. C22⋊PSU(3,𝔽2) | D3 | semidirect |
| 43. C2×PSU(3,𝔽2) | C2×D3 | semidirect |
| 51. #3777 | C2×D3 | semidirect |
| 52. C22×C33 | SD16 | semidirect |
| 57. C2×C3×C3⋊D3 | SD16 | semidirect |
| 116. C22×C32 | #215 | semidirect |
| 121. C2×C3⋊D3 | #215 | semidirect |
| 148. C33 | #450 | semidirect |
| 208. C22×C3 | AΓL(1,𝔽9) | semidirect |
| 231. C32 | #5046 | semidirect |
| 273. C22 | #89092 | semidirect |
| 280. C3 | #10596417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#157⋊D3 | 2 |
| C2×#89092 | 2 |
| C3×C22⋊PSU(3,𝔽2) | 2 |
| #11724243 | 2 |
| #11724101 | 2 |
| #10596417 | 3 |
| #5046 | 9 |