Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
240 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 17. #6189 | C4 | direct (N × H) |
| 34. C3×C4×C9 | Q8 | semidirect |
| 93. C4×C9 | Dic6 | semidirect |
| 101. C3×C9 | C4×Q8 | semidirect |
| 145. C3×C4 | Dic18 | semidirect |
| 159. C9 | C4×Dic6 | semidirect |
| 184. C4 | #6189 | direct (N × H) |
| 186. C3 | C4×Dic18 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6189 | 2 |
| C4×C3⋊Dic9 | 2 |
| C4×C9×Dic3 | 2 |
| C3×C4×Dic9 | 2 |
| Dic3⋊Dic9 | 2 |
| #88442 | 2 |
| Dic9⋊Dic3 | 2 |
| C4×#627 | 3 |
| C4×Dic18 | 3 |