Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
660 conjugacy classes of subgroups; only the 281 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 281 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. C22×C3⋊Dic9 | C2 | semidirect |
| 3. #88551 | C2 | direct (N × H) |
| 7. C23×C3×C9 | C4 | semidirect |
| 11. C2×C3⋊Dic9 | C22 | semidirect |
| 21. C22×C3×C9 | C2×C4 | semidirect |
| 34. C23×C9 | Dic3 | semidirect |
| 40. C2×C3×C9 | C22⋊C4 | semidirect |
| 59. C22×C9 | C2×Dic3 | semidirect |
| 64. C3×C9 | C2×C22⋊C4 | semidirect |
| 67. C23×C3 | Dic9 | semidirect |
| 82. C2×C9 | #217 | semidirect |
| 93. C22×C3 | C2×Dic9 | semidirect |
| 103. C9 | C2×#217 | semidirect |
| 105. C23 | C3⋊Dic9 | semidirect |
| 112. C2×C3 | #3676 | semidirect |
| 121. C22 | C2×C3⋊Dic9 | semidirect |
| 125. C3 | C2×#3676 | semidirect |
| 128. C2 | #88551 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C9 | 2 |
| C22×C3⋊Dic9 | 2 |
| #88551 | 2 |
| C2×#3757 | 3 |
| C2×#3676 | 3 |