Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1419 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1419 conjugacy classes of subgroups — too many to draw. Only its 299 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×#88434 | C2 | direct (N × H) |
| 10. C2×(C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 11. #88434 | C22 | direct (N × H) |
| 14. C22×C3⋊(C3⋊C8) | D3 | semidirect |
| 18. C22×#272 | C8 | semidirect |
| 25. (C3⋊(C3⋊C8))⋊C3 | C23 | semidirect |
| 38. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 41. C22×H(3,𝔽3) | C2×C8 | semidirect |
| 43. C2×#272 | C2×C8 | semidirect |
| 72. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 75. C2×H(3,𝔽3) | C22×C8 | semidirect |
| 77. #272 | C22×C8 | semidirect |
| 100. C22×C32 | D3×C8 | semidirect |
| 115. H(3,𝔽3) | C23×C8 | semidirect |
| 145. C2×C32 | C2×D3×C8 | semidirect |
| 178. C32 | C22×D3×C8 | semidirect |
| 199. C22 | #88434 | direct (N × H) |
| 208. C2 | C2×#88434 | 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×#88434 | 2 |
| C22×D3×C3⋊C8 | 3 |