Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1419 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 1419 conjugacy classes of subgroups — too many to draw. Only its 233 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. C2×C4⋊C4×H(3,𝔽3) | C2 | semidirect |
| 3. C2×#88542 | C2 | semidirect |
| 4. C2×C4×#1084 | C2 | semidirect |
| 12. C2×C4⋊#272 | C4 | semidirect |
| 17. C2×C32×C4⋊C4 | D3 | semidirect |
| 33. C2×#1084 | D4 | semidirect |
| 58. C4×H(3,𝔽3) | C22⋊C4 | semidirect |
| 121. C32×C4 | (C2×D3)⋊C4 | semidirect |
| 124. C2×C4⋊C4 | #272 | semidirect |
| 127. H(3,𝔽3) | #390 | semidirect |
| 200. C32 | #4988 | semidirect |
| 240. C4 | #88542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#272 | 2 |
| C2×C4⋊C4×H(3,𝔽3) | 2 |
| C2×#88542 | 2 |
| C2×C4×#1084 | 2 |
| C3×#4988 | 3 |