Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
572 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 306 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. C3×Q8×Dic3 | C3 | direct (N × H) |
| 6. C33×Q8 | C4 | semidirect |
| 20. C32×Dic3 | Q8 | direct (N × H) |
| 22. Q8×Dic3 | C32 | direct (N × H) |
| 24. C32×Q8 | Dic3 | direct (N × H) |
| 25. C32×Q8 | C3×C4 | semidirect |
| 52. C3×Dic3 | C3×Q8 | direct (N × H) |
| 54. C33 | C4×Q8 | semidirect |
| 56. C3×Q8 | C3×Dic3 | direct (N × H) |
| 57. C3×Q8 | C32×C4 | semidirect |
| 86. Dic3 | C32×Q8 | direct (N × H) |
| 88. C32 | Q8×Dic3 | direct (N × H) |
| 89. C32 | C3×C4×Q8 | semidirect |
| 90. Q8 | C32×Dic3 | direct (N × H) |
| 108. C3 | C3×Q8×Dic3 | direct (N × H) |
| 109. C3 | C32×C4×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q8 | 2 |
| C32×C4⋊Dic3 | 2 |
| C32×C4×Dic3 | 2 |
| C32×C4×Q8 | 3 |
| C3×Q8×Dic3 | 3 |