Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
594 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11721715 | C2 | semidirect |
| 3. H(3,𝔽3)×C4⋊C8 | C2 | semidirect |
| 5. #11720551 | C2 | semidirect |
| 18. C32×C4⋊C8 | D3 | semidirect |
| 28. C4⋊#272 | Q8 | semidirect |
| 110. C4⋊C8 | #272 | semidirect |
| 112. H(3,𝔽3) | #474 | semidirect |
| 168. C32 | #4846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#272 | 2 |
| #11721715 | 2 |
| H(3,𝔽3)×C4⋊C8 | 2 |
| #11720554 | 2 |
| #11720551 | 2 |
| C3×#4846 | 3 |