Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
292 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
| 3. #88435 | C2 | direct (N × H) |
| 10. (C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 13. C2×C3⋊(C3⋊C8) | D3 | semidirect |
| 34. C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 36. C2×H(3,𝔽3) | M16 | semidirect |
| 60. H(3,𝔽3) | C2×M16 | semidirect |
| 81. C2×C32 | ΓL(1,𝔽25) | semidirect |
| 107. C32 | C2×ΓL(1,𝔽25) | semidirect |
| 133. C2 | #88435 | direct (N × H) |
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 |
| #88435 | 2 |
| C2×#3711 | 3 |