Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
425 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 425 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #11720316 | C2 | semidirect |
| 108. H(3,𝔽3) | #430 | semidirect |
| 166. C32 | #5124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88538 | 2 |
| C2×#3748⋊C3 | 2 |
| #11720316 | 2 |
| #10591141 | 3 |