Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
560 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 162 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 | direct (N × H) |
| 26. C3×C3⋊Dic3 | Q8 | semidirect |
| 65. C3⋊Dic3 | C3×Q8 | semidirect |
| 69. C33 | C4⋊Q8 | semidirect |
| 109. C32 | #944 | semidirect |
| 110. C32 | C3×C4⋊Q8 | semidirect |
| 129. C3 | C3×#944 | semidirect |
| 130. C3 | #64153 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q8 | 2 |
| C2×C3×#634 | 2 |
| C3×#3750 | 2 |
| C3×C4×C3⋊Dic3 | 2 |
| #64153 | 3 |
| C3×#944 | 3 |