Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
177 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 177 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 9. (C3⋊(C3⋊C16))⋊C3 | C4 | semidirect |
| 33. C3⋊(C3⋊C16) | Dic3 | semidirect |
| 94. H(3,𝔽3) | #365 | semidirect |
| 140. C32 | #4487 | semidirect |
| 141. C32 | #4513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720552 | 2 |
| #63644⋊C3 | 2 |
| #63639⋊C3 | 2 |
| #10589138 | 3 |
| #10589137 | 3 |