Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
146 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 58 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. C4⋊#3771 | C3 | direct (N × H) |
| 23. C33×C4 | C16 | semidirect |
| 53. C32×C4 | C3×C16 | semidirect |
| 62. C33 | C4⋊C16 | semidirect |
| 94. C3×C4 | #3771 | semidirect |
| 100. C32 | C3×C4⋊C16 | semidirect |
| 120. C4 | C3×#3771 | semidirect |
| 123. C3 | C4⋊#3771 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3771 | 2 |
| C3×C4×#622 | 2 |
| C4⋊#3771 | 3 |
| C3×C4⋊C16 | 9 |