Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2739 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 2739 conjugacy classes of subgroups — too many to draw. Only its 261 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 |
|---|---|---|
| 1. C2×D4×#272 | C2 | semidirect |
| 2. H(3,𝔽3)×#127 | C2 | semidirect |
| 3. #11721850 | C2 | semidirect |
| 4. #11721720 | C2 | semidirect |
| 5. C42×#272 | C2 | semidirect |
| 8. C2×D4×H(3,𝔽3) | C22 | semidirect |
| 9. C2×#6235 | C22 | semidirect |
| 11. C2×C4⋊#272 | C22 | semidirect |
| 13. C42×H(3,𝔽3) | C22 | semidirect |
| 14. C4×#1084 | C22 | semidirect |
| 16. C32×#127 | D3 | semidirect |
| 29. C4×#272 | D4 | semidirect |
| 33. C2×C32×D4 | C2×D3 | semidirect |
| 38. C32×C42 | C2×D3 | semidirect |
| 45. C4×H(3,𝔽3) | C2×D4 | semidirect |
| 46. #1084 | C2×D4 | semidirect |
| 71. #272 | #127 | direct (N × H) |
| 93. C32×C4 | D3×D4 | semidirect |
| 98. #127 | #272 | direct (N × H) |
| 100. H(3,𝔽3) | C2×#127 | semidirect |
| 129. C2×D4 | C2×#272 | semidirect |
| 132. C42 | C2×#272 | semidirect |
| 147. C32 | D3×#127 | semidirect |
| 172. C4 | D4×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#272 | 2 |
| H(3,𝔽3)×#127 | 2 |
| #11721850 | 2 |
| #11721720 | 2 |
| C42×#272 | 2 |
| C3×D3×#127 | 3 |