Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
330 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 2. Q16×H(3,𝔽3) | C2 | semidirect |
| 3. #88550 | C2 | semidirect |
| 4. #88530 | C2 | semidirect |
| 15. C32×Q16 | D3 | semidirect |
| 34. #272 | Q16 | direct (N × H) |
| 51. H(3,𝔽3) | C2×Q16 | semidirect |
| 71. Q16 | #272 | direct (N × H) |
| 83. C32 | D3×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#272 | 2 |
| Q16×H(3,𝔽3) | 2 |
| #88550 | 2 |
| #88530 | 2 |
| C8×#272 | 2 |
| C3×D3×Q16 | 3 |