Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
715 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 715 conjugacy classes of subgroups — too many to draw. Only its 237 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. #11720520 | C2 | semidirect |
| 5. C4×#6180 | C2 | semidirect |
| 11. #88538 | C4 | semidirect |
| 12. C2×#6180 | C4 | semidirect |
| 101. H(3,𝔽3) | #405 | semidirect |
| 146. C32 | #4997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#117 | 2 |
| C2×#88538 | 2 |
| C22×#6180 | 2 |
| #11720520 | 2 |
| C4×#6180 | 2 |
| C3×#4997 | 3 |