Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
447 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #11720316 | C2 | direct (N × H) |
| 79. C2×H(3,𝔽3) | #108 | semidirect |
| 121. H(3,𝔽3) | C2×#108 | semidirect |
| 155. C2×C32 | #822 | semidirect |
| 189. C32 | C2×#822 | semidirect |
| 224. C2 | #11720316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6180 | 2 |
| C2×#3748⋊C3 | 2 |
| #11720316 | 2 |
| C2×#63577 | 3 |