Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 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. C3×C9×Q16 | C2 | semidirect |
| 3. #88547 | C2 | semidirect |
| 5. #88521 | C2 | semidirect |
| 21. C9×Q16 | D3 | semidirect |
| 47. C3⋊D9 | Q16 | direct (N × H) |
| 50. C3×Q16 | D9 | semidirect |
| 69. C3×C9 | C2×Q16 | semidirect |
| 91. Q16 | C3⋊D9 | direct (N × H) |
| 104. C9 | D3×Q16 | semidirect |
| 121. C3 | Q16×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊D9 | 2 |
| C3×C9×Q16 | 2 |
| #88547 | 2 |
| C8×C3⋊D9 | 2 |
| #88521 | 2 |
| Q16×C3⋊D3 | 3 |
| Q16×D9 | 3 |