Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
316 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 84 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×#611 | C2 | semidirect |
| 2. C2×C3×#611 | C2 | semidirect |
| 3. C2×C3×D36 | C2 | semidirect |
| 4. C2×C3×C4×D9 | C2 | semidirect |
| 5. C3×C9×C22⋊C4 | C2 | semidirect |
| 6. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 7. C3×Dic9⋊C4 | C2 | semidirect |
| 9. #63446 | C3 | direct (N × H) |
| 28. C2×#611 | C2×C3 | semidirect |
| 29. C2×#611 | C2×C3 | semidirect |
| 30. C2×D36 | C2×C3 | semidirect |
| 31. C2×C4×D9 | C2×C3 | semidirect |
| 33. C9×C22⋊C4 | C2×C3 | semidirect |
| 34. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 35. Dic9⋊C4 | C2×C3 | semidirect |
| 45. C2×C3×D9 | D4 | semidirect |
| 49. C3×Dic9 | D4 | semidirect |
| 94. C3×C22⋊C4 | D9 | semidirect |
| 125. C2×D9 | C3×D4 | semidirect |
| 131. Dic9 | C3×D4 | semidirect |
| 133. C3×C9 | #121 | semidirect |
| 181. C22⋊C4 | C3×D9 | semidirect |
| 218. C9 | C3×#121 | semidirect |
| 261. C3 | #63446 | 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 |
| C2×C3×D36 | 2 |
| C2×C3×C4×D9 | 2 |
| C3×C9×C22⋊C4 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| C3×Dic9⋊C4 | 2 |
| C3×#884 | 3 |
| #63446 | 3 |