Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
229 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 229 conjugacy classes of subgroups — too many to draw. Only its 50 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×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 11. C2×C3⋊(C3⋊C8) | D3 | semidirect |
| 16. C2×#272 | C8 | semidirect |
| 56. H(3,𝔽3) | C22⋊C8 | semidirect |
| 103. C32 | (C2×D3)⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#272 | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| (C2×D3)⋊(C3⋊C8) | 3 |