Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
594 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
| 3. C3×(C22⋊C9)⋊Q8 | C2 | semidirect |
| 5. Q8×(C22⋊C9)⋊C2 | C3 | direct (N × H) |
| 18. Q8×C22⋊C9 | C2×C3 | semidirect |
| 20. (C22⋊C9)⋊Q8 | C2×C3 | semidirect |
| 22. C3×(C22⋊C9)⋊C2 | Q8 | direct (N × H) |
| 48. C3×C22⋊C9 | C2×Q8 | semidirect |
| 53. C22×C3×Q8 | D9 | semidirect |
| 84. (C22⋊C9)⋊C2 | C3×Q8 | direct (N × H) |
| 136. C22⋊C9 | C2×C3×Q8 | semidirect |
| 141. C22×Q8 | C3×D9 | semidirect |
| 162. C3×Q8 | (C22⋊C9)⋊C2 | direct (N × H) |
| 217. C22×C3 | Q8×D9 | semidirect |
| 243. Q8 | C3×(C22⋊C9)⋊C2 | direct (N × H) |
| 269. C22 | C3×Q8×D9 | semidirect |
| 276. C3 | Q8×(C22⋊C9)⋊C2 | 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×(C22⋊C9)⋊Q8 | 2 |
| C3×Q8×#67 | 3 |
| Q8×(C22⋊C9)⋊C2 | 3 |
| C3×Q8×D9 | 4 |