Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
237 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 237 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. D4×#737 | C2 | semidirect |
| 2. C4⋊#4207 | C2 | semidirect |
| 3. #10619724 | C2 | semidirect |
| 4. #88544 | C3 | semidirect |
| 13. D4×3−1+2 | D3 | semidirect |
| 16. C3×D4×C9 | D3 | semidirect |
| 17. C3×D4×C9 | C2×C3 | semidirect |
| 18. C4⋊(C3⋊D9) | C2×C3 | semidirect |
| 22. C3⋊(C9⋊C8) | C2×C3 | semidirect |
| 51. #737 | D8 | semidirect |
| 108. 3−1+2 | #213 | semidirect |
| 111. C3×C9 | #213 | semidirect |
| 112. C3×C9 | C3×D8 | semidirect |
| 161. D4 | #4207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#737 | 2 |
| C4⋊#4207 | 2 |
| #10619724 | 2 |
| #88544 | 3 |
| #3673⋊C3 | 3 |
| #3753⋊C3 | 3 |
| C3×#3673 | 3 |