Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1903 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1903 conjugacy classes of subgroups — too many to draw. Only its 203 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×#88552 | C2 | semidirect |
| 3. C2×#3757⋊C3 | C2 | semidirect |
| 4. C2×#88450 | C2 | semidirect |
| 11. C23×(C3⋊D3)⋊C3 | C4 | semidirect |
| 13. C22×#1084 | C22 | semidirect |
| 14. C22×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 20. C2×#3757 | D3 | semidirect |
| 54. C23×C3⋊D3 | Dic3 | semidirect |
| 61. C22×C3⋊Dic3 | C2×D3 | semidirect |
| 76. C22×H(3,𝔽3) | C22⋊C4 | semidirect |
| 86. C2×(C3⋊D3)⋊C3 | C22⋊C4 | semidirect |
| 202. C22×C32 | (C2×D3)⋊C4 | semidirect |
| 203. C22×C32 | #217 | semidirect |
| 217. C2×C3⋊D3 | #217 | semidirect |
| 233. H(3,𝔽3) | #379 | semidirect |
| 381. C32 | #4955 | semidirect |
| 382. C32 | #5247 | semidirect |
| 433. C22 | #88450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×(C3⋊D3)⋊C3 | 2 |
| C2×#88552 | 2 |
| C2×#3757⋊C3 | 2 |
| C2×#88450 | 2 |
| #10591714 | 3 |
| #10591706 | 3 |