Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1279 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1279 conjugacy classes of subgroups — too many to draw. Only its 219 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×#634⋊C3 | C2 | semidirect |
| 3. C22×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 4. C2×#88437 | C2 | direct (N × H) |
| 13. C2×#634⋊C3 | C22 | semidirect |
| 14. C2×(C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 15. #88437 | C22 | direct (N × H) |
| 16. C22×#634 | D3 | semidirect |
| 21. C22×C3⋊(C3⋊C8) | D3 | semidirect |
| 34. #634⋊C3 | C23 | semidirect |
| 35. (C3⋊(C3⋊C8))⋊C3 | C23 | semidirect |
| 47. C2×#634 | C2×D3 | semidirect |
| 57. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 61. C22×H(3,𝔽3) | SD16 | semidirect |
| 98. #634 | C22×D3 | semidirect |
| 108. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 111. C2×H(3,𝔽3) | C2×SD16 | semidirect |
| 147. C22×C32 | #204 | semidirect |
| 148. C22×C32 | #215 | semidirect |
| 169. H(3,𝔽3) | C22×SD16 | semidirect |
| 212. C2×C32 | C2×#204 | semidirect |
| 213. C2×C32 | C2×#215 | semidirect |
| 256. C32 | C22×#204 | semidirect |
| 257. C32 | C22×#215 | semidirect |
| 283. C22 | #88437 | direct (N × H) |
| 293. C2 | C2×#88437 | 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×#634⋊C3 | 2 |
| C22×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C2×#88437 | 2 |
| C22×#3716 | 3 |
| C22×#3715 | 3 |