Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
680 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 5. C3×#4467 | C3 | direct (N × H) |
| 8. C2×C32×Dic6 | C4 | semidirect |
| 11. C32×C4⋊Dic3 | C4 | semidirect |
| 32. #4467 | C32 | direct (N × H) |
| 39. C2×C3×Dic6 | C3×C4 | semidirect |
| 47. C3×C4⋊Dic3 | C3×C4 | semidirect |
| 105. C2×Dic6 | C32×C4 | semidirect |
| 113. C4⋊Dic3 | C32×C4 | semidirect |
| 145. C33 | #328 | semidirect |
| 223. C32 | #4467 | direct (N × H) |
| 224. C32 | C3×#328 | semidirect |
| 262. C3 | C3×#4467 | direct (N × H) |
| 263. C3 | C32×#328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#924 | 2 |
| C33×C22⋊C8 | 2 |
| C32×C3⋊#95 | 2 |
| C32×#328 | 3 |
| C3×#4467 | 3 |