Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
618 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 82 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. C3×Q8×C22⋊C9 | C2 | semidirect |
| 2. C3×C4⋊((C22⋊C9)⋊C2) | C2 | semidirect |
| 3. C3×C4×(C22⋊C9)⋊C2 | C2 | semidirect |
| 5. #10593094 | C3 | direct (N × H) |
| 18. Q8×C22⋊C9 | C2×C3 | semidirect |
| 19. C4⋊((C22⋊C9)⋊C2) | C2×C3 | semidirect |
| 20. C4×(C22⋊C9)⋊C2 | C2×C3 | semidirect |
| 48. C3×C22⋊C9 | #41 | semidirect |
| 53. C22×C3×Q8 | D9 | semidirect |
| 136. C22⋊C9 | C3×#41 | semidirect |
| 141. C22×Q8 | C3×D9 | semidirect |
| 160. C3×Q8 | (C22⋊C9)⋊C2 | semidirect |
| 217. C22×C3 | #3701 | semidirect |
| 241. Q8 | C3×(C22⋊C9)⋊C2 | semidirect |
| 269. C22 | C3×#3701 | semidirect |
| 276. C3 | #10593094 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×C22⋊C9 | 2 |
| C3×C4⋊((C22⋊C9)⋊C2) | 2 |
| C3×C4×(C22⋊C9)⋊C2 | 2 |
| C3×#5817 | 3 |
| #10593094 | 3 |
| C3×#3701 | 4 |