Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
330 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×#6229 | C2 | semidirect |
| 3. M16×H(3,𝔽3) | C2 | semidirect |
| 4. #88530 | C2 | semidirect |
| 5. #88528 | C2 | semidirect |
| 21. C32×M16 | D3 | semidirect |
| 22. C32×M16 | D3 | semidirect |
| 85. H(3,𝔽3) | #137 | semidirect |
| 123. M16 | #272 | semidirect |
| 142. C32 | #909 | semidirect |
| 143. C32 | #909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88740 | 2 |
| C2×#6229 | 2 |
| M16×H(3,𝔽3) | 2 |
| #88530 | 2 |
| #88528 | 2 |
| C3×#909 | 3 |