Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
711 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 711 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. Q8×#1088 | C2 | semidirect |
| 4. C2×Q8×H(3,𝔽3) | C4 | semidirect |
| 5. Q8×#272 | C4 | semidirect |
| 8. C2×#6229 | C4 | semidirect |
| 72. H(3,𝔽3) | #519 | semidirect |
| 95. C2×Q8 | #1088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#272 | 2 |
| Q8×#1088 | 2 |
| #11722448 | 2 |
| C3×#519 | 9 |