Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 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. #88551 | C2 | semidirect |
| 5. C23×C3×C9 | C4 | semidirect |
| 8. C2×C3×C4×C9 | C4 | semidirect |
| 28. C23×C9 | Dic3 | semidirect |
| 31. C2×C4×C9 | Dic3 | semidirect |
| 56. C3×C9 | #99 | semidirect |
| 57. C23×C3 | Dic9 | semidirect |
| 63. C2×C3×C4 | Dic9 | semidirect |
| 92. C9 | #834 | semidirect |
| 93. C23 | C3⋊Dic9 | semidirect |
| 97. C2×C4 | C3⋊Dic9 | semidirect |
| 113. C3 | #63393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| #88551 | 2 |
| #63661 | 3 |
| #63393 | 3 |