Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
594 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 594 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 |
|---|---|---|
| 49. C4×H(3,𝔽3) | Q16 | semidirect |
| 102. C32×C4 | #216 | semidirect |
| 111. H(3,𝔽3) | #462 | semidirect |
| 163. C32 | #5031 | semidirect |
| 186. C4 | #88550 | 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 |
| C2×#88550 | 2 |
| #11721715 | 2 |
| #11720532 | 2 |
| C4⋊#6180 | 2 |
| C3×#5031 | 3 |