Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
283 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 283 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. Q8×C3⋊Dic3 | C3 | semidirect |
| 6. Q8×H(3,𝔽3) | C4 | semidirect |
| 20. (C3⋊Dic3)⋊C3 | Q8 | direct (N × H) |
| 25. C32×Q8 | Dic3 | semidirect |
| 26. C32×Q8 | C3×C4 | semidirect |
| 54. C3⋊Dic3 | C3×Q8 | semidirect |
| 58. H(3,𝔽3) | C4×Q8 | semidirect |
| 100. C32 | Q8×Dic3 | semidirect |
| 101. C32 | C3×C4×Q8 | semidirect |
| 102. Q8 | (C3⋊Dic3)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×H(3,𝔽3) | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| Q8×C3⋊Dic3 | 3 |
| C3×Q8×Dic3 | 3 |