Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
300 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 121 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. #88547 | C2 | direct (N × H) |
| 46. C2×C3×C9 | Q16 | semidirect |
| 67. C3×C9 | C2×Q16 | semidirect |
| 86. C2×C9 | #216 | semidirect |
| 103. C9 | C2×#216 | semidirect |
| 112. C2×C3 | #3674 | semidirect |
| 121. C3 | C2×#3674 | semidirect |
| 123. C2 | #88547 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C9 | 2 |
| C2×#6226 | 2 |
| #88547 | 2 |
| C2×C3⋊(C9⋊C8) | 2 |
| C2×#3756 | 3 |
| C2×#3674 | 3 |