Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1279 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1279 conjugacy classes of subgroups — too many to draw. Only its 259 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. C22×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 3. C2×#88435 | C2 | direct (N × H) |
| 10. C2×(C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 11. #88435 | C22 | direct (N × H) |
| 14. C22×C3⋊(C3⋊C8) | D3 | semidirect |
| 25. (C3⋊(C3⋊C8))⋊C3 | C23 | semidirect |
| 38. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 41. C22×H(3,𝔽3) | M16 | semidirect |
| 72. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 75. C2×H(3,𝔽3) | C2×M16 | semidirect |
| 100. C22×C32 | ΓL(1,𝔽25) | semidirect |
| 115. H(3,𝔽3) | C22×M16 | semidirect |
| 145. C2×C32 | C2×ΓL(1,𝔽25) | semidirect |
| 178. C32 | C22×ΓL(1,𝔽25) | semidirect |
| 199. C22 | #88435 | direct (N × H) |
| 208. C2 | C2×#88435 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#272 | 2 |
| C22×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C2×#88435 | 2 |
| C22×#3711 | 3 |