Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2044 conjugacy classes of subgroups; only the 851 normal subgroups are shown.
This group has 2044 conjugacy classes of subgroups — too many to draw. Only its 851 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. #11722206 | C2 | direct (N × H) |
| 62. C2×C33 | #101 | semidirect |
| 83. C33 | C2×#101 | semidirect |
| 97. C2×C32 | #836 | semidirect |
| 115. C32 | C2×#836 | semidirect |
| 129. C2×C3 | #63663 | semidirect |
| 138. C3 | C2×#63663 | semidirect |
| 141. C2 | #11722206 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| C2×#88855 | 2 |
| #11722206 | 2 |
| C2×#63663 | 3 |