Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1419 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1419 conjugacy classes of subgroups — too many to draw. Only its 277 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×C42×H(3,𝔽3) | C2 | semidirect |
| 4. C2×C4×#1084 | C2 | semidirect |
| 5. #11720574 | C2 | semidirect |
| 14. C2×C4×#272 | C4 | semidirect |
| 16. #88542 | C4 | direct (N × H) |
| 19. C2×C32×C42 | D3 | semidirect |
| 32. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 40. C2×#1084 | C2×C4 | semidirect |
| 64. C2×#272 | C42 | semidirect |
| 66. C4×H(3,𝔽3) | C22⋊C4 | semidirect |
| 88. C2×C32×C4 | C4×D3 | semidirect |
| 138. C32×C4 | (C2×D3)⋊C4 | semidirect |
| 144. C2×C42 | #272 | semidirect |
| 146. H(3,𝔽3) | C4×C22⋊C4 | semidirect |
| 230. C32 | C4×(C2×D3)⋊C4 | semidirect |
| 247. C2×C4 | C4×#272 | semidirect |
| 275. C4 | #88542 | 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 |
| C2×C42×H(3,𝔽3) | 2 |
| C2×#88542 | 2 |
| C2×C4×#1084 | 2 |
| #11720574 | 2 |
| C3×C4×(C2×D3)⋊C4 | 3 |