Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1287 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 1287 conjugacy classes of subgroups — too many to draw. Only its 257 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 |
|---|---|---|
| 4. C2×#88540 | C2 | semidirect |
| 5. #11720574 | C2 | semidirect |
| 15. #88552 | C4 | semidirect |
| 38. C2×#1084 | C2×C4 | semidirect |
| 55. C22×H(3,𝔽3) | C4⋊C4 | semidirect |
| 123. C22×C32 | Dic3⋊C4 | semidirect |
| 138. H(3,𝔽3) | #385 | semidirect |
| 217. C32 | #5210 | semidirect |
| 251. C22 | #88540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×H(3,𝔽3) | 2 |
| C2×#88552 | 2 |
| C2×#88540 | 2 |
| #11720574 | 2 |
| C3×#5210 | 3 |