Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
318 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 51 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. C22×C3⋊AGL(1,𝔽9) | C2 | semidirect |
| 2. C2×#89092 | C2 | semidirect |
| 3. C3×C22⋊PSU(3,𝔽2) | C2 | semidirect |
| 5. #11724103 | C2 | semidirect |
| 6. #11724102 | C2 | semidirect |
| 7. #11724101 | C2 | semidirect |
| 24. C22⋊PSU(3,𝔽2) | D3 | semidirect |
| 42. C3⋊AGL(1,𝔽9) | D4 | semidirect |
| 61. C22×C33 | SD16 | semidirect |
| 65. C2×C3×C3⋊D3 | SD16 | semidirect |
| 130. C22×C32 | #215 | semidirect |
| 134. C2×C3⋊D3 | #215 | semidirect |
| 163. C33 | #465 | semidirect |
| 225. C22×C3 | AΓL(1,𝔽9) | semidirect |
| 248. C32 | #5048 | semidirect |
| 289. C22 | #89092 | semidirect |
| 298. C3 | #10596416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊AGL(1,𝔽9) | 2 |
| C2×#89092 | 2 |
| C3×C22⋊PSU(3,𝔽2) | 2 |
| #11724355 | 2 |
| #11724103 | 2 |
| #11724102 | 2 |
| #11724101 | 2 |
| #10596416 | 3 |
| #5048 | 9 |