Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
266 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. C2×C3×Q8×C9 | C2 | semidirect |
| 3. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 4. C3×C4×Dic9 | C2 | semidirect |
| 6. #63509 | C3 | direct (N × H) |
| 18. C2×Q8×C9 | C2×C3 | semidirect |
| 20. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 21. C4×Dic9 | C2×C3 | semidirect |
| 49. C2×C3×Q8 | D9 | semidirect |
| 73. C3×C9 | #124 | semidirect |
| 97. C2×Q8 | C3×D9 | semidirect |
| 118. C9 | C3×#124 | semidirect |
| 140. C3 | #63509 | 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×C3×D36 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| C3×C4×Dic9 | 2 |
| C3×#947 | 3 |
| #63509 | 3 |