Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
268 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 268 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 |
|---|---|---|
| 2. C22×C3×Dic9 | C2 | semidirect |
| 3. C3×C9×C22⋊C4 | C2 | semidirect |
| 4. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic9 | C2 | semidirect |
| 7. #63448 | C3 | direct (N × H) |
| 21. C22×Dic9 | C2×C3 | semidirect |
| 23. C9×C22⋊C4 | C2×C3 | semidirect |
| 24. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 25. C4⋊Dic9 | C2×C3 | semidirect |
| 63. C3×C22⋊C4 | D9 | semidirect |
| 88. C3×C9 | #123 | semidirect |
| 120. C22⋊C4 | C3×D9 | semidirect |
| 143. C9 | C3×#123 | semidirect |
| 171. C3 | #63448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#611 | 2 |
| C22×C3×Dic9 | 2 |
| C3×C9×C22⋊C4 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| C3×C4⋊Dic9 | 2 |
| C3×#886 | 3 |
| #63448 | 3 |