Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×(C3⋊D9)⋊C4 | C2 | semidirect |
| 3. C9×C4⋊Dic3 | C2 | semidirect |
| 4. C3×C4×Dic9 | C2 | semidirect |
| 5. #88445 | C2 | semidirect |
| 10. C4⋊(C3⋊D9) | C4 | semidirect |
| 25. C4×Dic9 | D3 | semidirect |
| 29. C2×C3⋊D9 | C2×C4 | semidirect |
| 30. C3×C4×C9 | C2×C4 | semidirect |
| 33. C3×Dic9 | D4 | semidirect |
| 66. C4⋊Dic3 | D9 | semidirect |
| 86. C4×C9 | C4×D3 | semidirect |
| 88. Dic9 | D12 | semidirect |
| 90. C3×C9 | C4×D4 | semidirect |
| 141. C3×C4 | C4×D9 | semidirect |
| 148. C9 | C4×D12 | semidirect |
| 175. C4 | (C3⋊D9)⋊C4 | semidirect |
| 177. C3 | #63455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D9) | 2 |
| C2×(C3⋊D9)⋊C4 | 2 |
| C9×C4⋊Dic3 | 2 |
| C3×C4×Dic9 | 2 |
| #88445 | 2 |
| #63894 | 3 |
| #63455 | 3 |