Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
288 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 288 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. C22×C3×C4×C9 | C2 | semidirect |
| 3. C3×#3676 | C2 | semidirect |
| 4. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 5. C3×Dic9⋊C4 | C2 | semidirect |
| 7. #63491 | C3 | direct (N × H) |
| 21. C22×C4×C9 | C2×C3 | semidirect |
| 23. #3676 | C2×C3 | semidirect |
| 24. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 25. Dic9⋊C4 | C2×C3 | semidirect |
| 59. C22×C3×C4 | D9 | semidirect |
| 89. C3×C9 | #123 | semidirect |
| 119. C22×C4 | C3×D9 | semidirect |
| 145. C9 | C3×#123 | semidirect |
| 173. C3 | #63491 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C9 | 2 |
| C2×C3×#611 | 2 |
| C3×#3676 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| C3×Dic9⋊C4 | 2 |
| C3×#929 | 3 |
| #63491 | 3 |