Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1617 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1617 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×#88740 | C2 | semidirect |
| 2. C2×C4⋊C4×H(3,𝔽3) | C2 | semidirect |
| 3. #11721830 | C2 | semidirect |
| 4. #11721765 | C2 | semidirect |
| 5. #11721763 | C2 | semidirect |
| 19. C2×C32×C4⋊C4 | D3 | semidirect |
| 26. C2×C4×H(3,𝔽3) | D4 | semidirect |
| 71. C2×C32×C4 | D12 | semidirect |
| 122. C2×C4⋊C4 | #272 | semidirect |
| 123. H(3,𝔽3) | #537 | semidirect |
| 184. C32 | #5510 | semidirect |
| 194. C2×C4 | C4⋊#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88740 | 2 |
| C2×C4⋊C4×H(3,𝔽3) | 2 |
| #11721830 | 2 |
| #11721765 | 2 |
| #11721763 | 2 |
| C3×#5510 | 3 |