Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
222 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 87 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. Q8×C92 | C2 | semidirect |
| 2. C9×D36 | C2 | semidirect |
| 3. C4×C9×D9 | C2 | semidirect |
| 20. #3701 | C9 | direct (N × H) |
| 28. C92 | #41 | semidirect |
| 35. Q8×C9 | D9 | semidirect |
| 36. Q8×C9 | C2×C9 | semidirect |
| 39. D36 | C2×C9 | semidirect |
| 40. C4×D9 | C2×C9 | semidirect |
| 91. C9 | #3701 | direct (N × H) |
| 92. C9 | C9×#41 | semidirect |
| 93. Q8 | C9×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C92 | 2 |
| C9×D36 | 2 |
| C4×C9×D9 | 2 |
| C9×#239 | 3 |
| C3×#3701 | 3 |