Finite Group DatabasebetaFinite Group DatabasebetaOrder 3456.
759 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 759 conjugacy classes of subgroups — too many to draw. Only its 167 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. #10588377⋊C3 | C2 | semidirect |
| 2. #10588377⋊C3 | C2 | semidirect |
| 3. #10588376⋊C3 | C2 | semidirect |
| 4. #10588375⋊C3 | C2 | semidirect |
| 5. 3−1+2×#322 | C2 | semidirect |
| 7. #11782905 | C3 | semidirect |
| 22. #10588377 | C2×C3 | semidirect |
| 23. #10588377 | C2×C3 | semidirect |
| 24. #10588376 | C2×C3 | semidirect |
| 25. #10588375 | C2×C3 | semidirect |
| 27. C9×#322 | C2×C3 | semidirect |
| 75. C8×3−1+2 | D8 | semidirect |
| 172. C8×C9 | C3×D8 | semidirect |
| 177. #322 | AGL(1,ℤ/9) | semidirect |
| 238. 3−1+2 | #1721 | semidirect |
| 308. C9 | C3×#1721 | semidirect |
| 321. C8 | D72⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588377⋊C3 | 2 |
| #10588376⋊C3 | 2 |
| #10588375⋊C3 | 2 |
| 3−1+2×#322 | 2 |
| C3×#68094 | 3 |
| #11782905 | 3 |