Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
451 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 451 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11720570 | C2 | direct (N × H) |
| 60. C2×H(3,𝔽3) | Q32 | semidirect |
| 87. H(3,𝔽3) | C2×Q32 | semidirect |
| 106. C2×C32 | #829 | semidirect |
| 126. C32 | C2×#829 | semidirect |
| 147. C2 | #11720570 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×H(3,𝔽3) | 2 |
| C2×#88530 | 2 |
| #11720570 | 2 |
| C2×#88386 | 2 |
| C2×C3×#829 | 3 |