Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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×#731 | C2 | semidirect |
| 2. C4⋊#4177 | C2 | semidirect |
| 3. C4×#4177 | C2 | semidirect |
| 4. #88746 | C3 | semidirect |
| 11. C3×Q8×C9 | C2×C3 | semidirect |
| 12. C4⋊(C3⋊D9) | C2×C3 | semidirect |
| 13. C4×C3⋊D9 | C2×C3 | semidirect |
| 28. #731 | #41 | semidirect |
| 59. C3×C9 | C3×#41 | semidirect |
| 90. Q8 | #4177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#731 | 2 |
| C4⋊#4177 | 2 |
| C4×#4177 | 2 |
| #88746 | 3 |
| #88722 | 3 |