Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
391 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 391 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 13. #3748⋊C3 | C4 | semidirect |
| 15. C2×(C3⋊(C3⋊C8))⋊C3 | C4 | semidirect |
| 42. #3748 | Dic3 | semidirect |
| 44. C2×C3⋊(C3⋊C8) | Dic3 | semidirect |
| 176. H(3,𝔽3) | #344 | semidirect |
| 274. C32 | #4556 | semidirect |
| 275. C32 | #4559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721826 | 2 |
| C2×#3748⋊C3 | 2 |
| #10589170 | 3 |
| #10589169 | 3 |