Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
303 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. C4⋊(3−1+2⋊C4) | C2 | direct (N × H) |
| 5. C2×C4⋊Dic9 | C3 | semidirect |
| 7. C2×C4×3−1+2 | C4 | semidirect |
| 17. C4⋊Dic9 | C2×C3 | semidirect |
| 22. C4×3−1+2 | C2×C4 | semidirect |
| 35. C2×C4×C9 | C3×C4 | semidirect |
| 39. C2×3−1+2 | C4⋊C4 | semidirect |
| 64. C4×C9 | C2×C3×C4 | semidirect |
| 67. 3−1+2 | C2×C4⋊C4 | semidirect |
| 86. C2×C9 | C3×C4⋊C4 | semidirect |
| 107. C9 | C2×C3×C4⋊C4 | semidirect |
| 111. C2×C4 | 3−1+2⋊C4 | semidirect |
| 126. C4 | C2×3−1+2⋊C4 | semidirect |
| 129. C2 | C4⋊(3−1+2⋊C4) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×3−1+2 | 2 |
| C22×3−1+2⋊C4 | 2 |
| C4⋊(3−1+2⋊C4) | 2 |
| C2×C3×C4⋊Dic3 | 3 |
| C2×C4⋊Dic9 | 3 |