Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
276 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 5. #64153 | C3 | semidirect |
| 26. (C3⋊Dic3)⋊C3 | Q8 | semidirect |
| 70. C3⋊Dic3 | C3×Q8 | semidirect |
| 74. H(3,𝔽3) | C4⋊Q8 | semidirect |
| 125. C32 | #944 | semidirect |
| 126. C32 | C3×C4⋊Q8 | semidirect |
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 |
| C2×#634⋊C3 | 2 |
| #3750⋊C3 | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| #64153 | 3 |
| C3×#944 | 3 |