Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
220 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 3. C3×#3776 | C2 | semidirect |
| 4. #64228 | C3 | direct (N × H) |
| 13. #3776 | C2×C3 | semidirect |
| 31. C3×C3⋊D3 | Q16 | semidirect |
| 48. C33 | C2×Q16 | semidirect |
| 63. C3⋊D3 | C3×Q16 | semidirect |
| 81. C32 | C2×C3×Q16 | semidirect |
| 98. C3 | #64228 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3797 | 2 |
| C3×#3787 | 2 |
| C3×#3776 | 2 |
| #64228 | 3 |
| C2×C3×Q16 | 9 |