Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
759 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 759 conjugacy classes of subgroups — too many to draw. Only its 175 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 | direct (N × H) |
| 7. C2×Q8×H(3,𝔽3) | C4 | semidirect |
| 8. Q8×#272 | C4 | semidirect |
| 11. C2×#6229 | C4 | semidirect |
| 17. C2×#1088 | Q8 | direct (N × H) |
| 20. Q8×H(3,𝔽3) | C2×C4 | semidirect |
| 25. #6229 | C2×C4 | semidirect |
| 38. #1088 | C2×Q8 | direct (N × H) |
| 54. C2×H(3,𝔽3) | C4×Q8 | semidirect |
| 56. #272 | C4×Q8 | semidirect |
| 84. H(3,𝔽3) | C2×C4×Q8 | semidirect |
| 111. C2×Q8 | #1088 | direct (N × H) |
| 136. Q8 | C2×#1088 | direct (N × H) |
| 169. C2 | Q8×#1088 | direct (N × H) |
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 |
| C2×C4⋊#1088 | 2 |
| C2×C4×#1088 | 2 |
| C2×C3×C4×Q8 | 9 |