Finite Group DatabasebetaFinite Group Databasebeta← (C2×AGL(1,ℤ/9))⋊C8 #11720439
Order 864.
161 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 161 conjugacy classes of subgroups — too many to draw. Only its 59 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×C8×3−1+2 | C2 | semidirect |
| 3. C2×3−1+2⋊C8 | C2 | semidirect |
| 5. (C2×D9)⋊C8 | C3 | semidirect |
| 18. C2×C8×C9 | C2×C3 | semidirect |
| 19. C2×C9⋊C8 | C2×C3 | semidirect |
| 23. C2×AGL(1,ℤ/9) | C8 | semidirect |
| 66. C2×D9 | C3×C8 | semidirect |
| 73. 3−1+2 | C22⋊C8 | semidirect |
| 101. C2×C8 | AGL(1,ℤ/9) | semidirect |
| 118. C9 | C3×C22⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×AGL(1,ℤ/9) | 2 |
| C2×C8×3−1+2 | 2 |
| C2×3−1+2⋊C8 | 2 |
| C3×(C2×D3)⋊C8 | 3 |
| (C2×D9)⋊C8 | 3 |