Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
561 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 561 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11721716 | C2 | semidirect |
| 3. H(3,𝔽3)×C4⋊C8 | C2 | semidirect |
| 6. #11720551 | C2 | semidirect |
| 7. #11720550 | C2 | semidirect |
| 22. C32×C4⋊C8 | D3 | semidirect |
| 131. C4⋊C8 | #272 | semidirect |
| 134. H(3,𝔽3) | #478 | semidirect |
| 196. C32 | #4847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#272 | 2 |
| #11721716 | 2 |
| H(3,𝔽3)×C4⋊C8 | 2 |
| #11720554 | 2 |
| #11720551 | 2 |
| #11720550 | 2 |
| C3×#4847 | 3 |