Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
206 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 111 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. C3×C9×M16 | C2 | semidirect |
| 3. C2×C9×C3⋊C8 | C2 | semidirect |
| 4. C9×ΓL(1,𝔽25) | C2 | semidirect |
| 5. D3×C8×C9 | C2 | semidirect |
| 24. C9×M16 | D3 | semidirect |
| 33. #907 | C9 | direct (N × H) |
| 59. C3×M16 | C2×C9 | semidirect |
| 63. C2×C3⋊C8 | C2×C9 | semidirect |
| 64. ΓL(1,𝔽25) | C2×C9 | semidirect |
| 65. D3×C8 | C2×C9 | semidirect |
| 80. C3×C9 | #131 | semidirect |
| 109. M16 | D3×C9 | semidirect |
| 127. C9 | #907 | direct (N × H) |
| 150. C3 | C9×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#235 | 2 |
| C3×C9×M16 | 2 |
| C2×C9×C3⋊C8 | 2 |
| C9×ΓL(1,𝔽25) | 2 |
| D3×C8×C9 | 2 |
| C3×#907 | 3 |
| C9×#131 | 3 |