Finite Group DatabasebetaFinite Group DatabasebetaOrder 3456.
797 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 797 conjugacy classes of subgroups — too many to draw. Only its 155 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. 3−1+2×#492 | C2 | semidirect |
| 2. #10588773⋊C3 | C2 | semidirect |
| 3. #10588755⋊C3 | C2 | semidirect |
| 4. #10588377⋊C3 | C2 | semidirect |
| 5. #10588132⋊C3 | C2 | semidirect |
| 7. #11782899 | C3 | semidirect |
| 23. C9×#492 | C2×C3 | semidirect |
| 24. #10588773 | C2×C3 | semidirect |
| 25. #10588755 | C2×C3 | semidirect |
| 26. #10588377 | C2×C3 | semidirect |
| 27. #10588132 | C2×C3 | semidirect |
| 76. C8×3−1+2 | D8 | semidirect |
| 181. C8×C9 | C3×D8 | semidirect |
| 185. #492 | AGL(1,ℤ/9) | semidirect |
| 251. 3−1+2 | #1721 | semidirect |
| 322. C9 | C3×#1721 | semidirect |
| 335. C8 | #3673⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#492 | 2 |
| #10588773⋊C3 | 2 |
| #10588755⋊C3 | 2 |
| #10588377⋊C3 | 2 |
| #10588132⋊C3 | 2 |
| C3×#71262 | 3 |
| #11782899 | 3 |