Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
394 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 106 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×C4⋊Q8 | C2 | semidirect |
| 4. #63395⋊C3 | C2 | semidirect |
| 5. C4⋊(3−1+2⋊C8) | C2 | semidirect |
| 7. #10588768 | C3 | semidirect |
| 24. C9×C4⋊Q8 | C2×C3 | semidirect |
| 27. #63395 | C2×C3 | semidirect |
| 28. C4⋊(C9⋊C8) | C2×C3 | semidirect |
| 73. C4×3−1+2 | SD16 | semidirect |
| 164. C4×C9 | C3×SD16 | semidirect |
| 169. C4⋊Q8 | AGL(1,ℤ/9) | semidirect |
| 173. 3−1+2 | #461 | semidirect |
| 241. C9 | C3×#461 | semidirect |
| 269. C4 | #3675⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×C4⋊Q8 | 2 |
| C2×#3675⋊C3 | 2 |
| C4×C4⋊AGL(1,ℤ/9) | 2 |
| #63395⋊C3 | 2 |
| C4⋊(3−1+2⋊C8) | 2 |
| C3×#5083 | 3 |
| #10588768 | 3 |