Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
362 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #11722579 | C2 | semidirect |
| 2. #11721359 | C2 | semidirect |
| 4. #578⋊C9 | C3 | semidirect |
| 13. 2−1+4⋊C9 | C2×C3 | semidirect |
| 14. #131⋊C9 | C2×C3 | semidirect |
| 60. #578 | 3−1+2 | semidirect |
| 92. 2−1+4 | C2×3−1+2 | semidirect |
| 96. #131 | C2×3−1+2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722579 | 2 |
| #11721359 | 2 |
| C32×#578 | 3 |
| #578⋊C9 | 3 |
| D8×3−1+2 | 4 |