Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
285 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 12. Q16×H(3,𝔽3) | C4 | semidirect |
| 13. #88550 | C4 | semidirect |
| 14. #88530 | C4 | semidirect |
| 37. #1088 | Q16 | direct (N × H) |
| 84. H(3,𝔽3) | C4×Q16 | semidirect |
| 109. Q16 | #1088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1088 | 2 |
| Q16×#272 | 2 |
| #11720790 | 2 |
| #11720775 | 2 |
| C8×#1088 | 2 |
| C3×C4×Q16 | 9 |