Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
693 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 693 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. H(3,𝔽3)×C4⋊C8 | C2 | semidirect |
| 4. #11720547 | C2 | semidirect |
| 5. C4⋊#6180 | C2 | semidirect |
| 19. C32×C4⋊C8 | D3 | semidirect |
| 52. C4×H(3,𝔽3) | M16 | semidirect |
| 57. #1084 | M16 | semidirect |
| 111. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 121. C4⋊C8 | #272 | semidirect |
| 122. H(3,𝔽3) | #423 | semidirect |
| 185. C32 | #4837 | semidirect |
| 215. C4 | #88527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88527 | 2 |
| C42×#272 | 2 |
| H(3,𝔽3)×C4⋊C8 | 2 |
| #11720547 | 2 |
| C4⋊#6180 | 2 |
| C3×#4837 | 3 |