Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
528 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 22. Q8×H(3,𝔽3) | Q8 | semidirect |
| 61. C32×Q8 | Dic6 | semidirect |
| 105. H(3,𝔽3) | #477 | semidirect |
| 154. C32 | #5021 | semidirect |
| 157. Q8 | #6229 | semidirect |
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 |
| #11721715 | 2 |
| #11720583 | 2 |
| #11720529 | 2 |
| C4⋊#6180 | 2 |
| C3×#5021 | 3 |