Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
226 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 95 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×C3⋊(C9⋊C8) | C2 | semidirect |
| 3. C2×C3×C9⋊C8 | C2 | semidirect |
| 4. #88420 | C2 | direct (N × H) |
| 12. C3⋊(C9⋊C8) | C22 | semidirect |
| 13. C3×C9⋊C8 | C22 | semidirect |
| 22. C2×C9⋊C8 | D3 | semidirect |
| 46. C9⋊C8 | C2×D3 | semidirect |
| 47. C2×C3×C9 | M16 | semidirect |
| 75. C3×C9 | C2×M16 | semidirect |
| 98. C2×C9 | ΓL(1,𝔽25) | semidirect |
| 121. C9 | C2×ΓL(1,𝔽25) | semidirect |
| 132. C2×C3 | #3667 | semidirect |
| 144. C3 | C2×#3667 | semidirect |
| 147. C2 | #88420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C9 | 2 |
| C2×C3⋊(C9⋊C8) | 2 |
| C2×C3×C9⋊C8 | 2 |
| #88420 | 2 |
| C2×#3711 | 3 |
| C2×#3667 | 3 |