Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
385 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 385 conjugacy classes of subgroups — too many to draw. Only its 146 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 |
|---|---|---|
| 6. Q8×H(3,𝔽3) | C4 | semidirect |
| 19. #1084 | Q8 | direct (N × H) |
| 23. C32×Q8 | Dic3 | semidirect |
| 24. C32×Q8 | Dic3 | semidirect |
| 52. H(3,𝔽3) | C4×Q8 | semidirect |
| 86. C32 | Q8×Dic3 | semidirect |
| 87. C32 | Q8×Dic3 | semidirect |
| 88. Q8 | #1084 | 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⋊#1084 | 2 |
| C4×#1084 | 2 |
| C3×Q8×Dic3 | 3 |