Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
561 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 561 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 13. Q8×H(3,𝔽3) | C8 | semidirect |
| 18. #6180 | Q8 | direct (N × H) |
| 37. C32×Q8 | C3⋊C8 | semidirect |
| 65. H(3,𝔽3) | C8×Q8 | semidirect |
| 96. C32 | Q8×C3⋊C8 | semidirect |
| 97. Q8 | #6180 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×H(3,𝔽3) | 2 |
| C4⋊#6180 | 2 |
| C4×#6180 | 2 |
| C3×Q8×C3⋊C8 | 3 |