Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
341 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 82 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. M16×H(3,𝔽3) | C2 | semidirect |
| 3. C2×#6180 | C2 | semidirect |
| 4. #88527 | C2 | semidirect |
| 5. C8×#272 | C2 | semidirect |
| 16. C32×M16 | D3 | semidirect |
| 54. H(3,𝔽3) | #131 | semidirect |
| 76. M16 | #272 | semidirect |
| 89. C32 | #907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88740 | 2 |
| M16×H(3,𝔽3) | 2 |
| C2×#6180 | 2 |
| #88527 | 2 |
| C8×#272 | 2 |
| C3×#907 | 3 |