Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1123 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1123 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 4. #11721099 | C2 | direct (N × H) |
| 22. C2×#1084 | Q8 | semidirect |
| 46. #1084 | C2×Q8 | semidirect |
| 75. C2×H(3,𝔽3) | C4⋊Q8 | semidirect |
| 114. H(3,𝔽3) | C2×C4⋊Q8 | semidirect |
| 142. C2×C32 | #944 | semidirect |
| 171. C32 | C2×#944 | semidirect |
| 198. C2 | #11721099 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#634⋊C3 | 2 |
| C2×C4×#1084 | 2 |
| C2×#88449 | 2 |
| #11721099 | 2 |
| C2×#63866 | 3 |