Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
803 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 803 conjugacy classes of subgroups — too many to draw. Only its 221 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. #11720584 | C2 | direct (N × H) |
| 66. C2×H(3,𝔽3) | #101 | semidirect |
| 96. H(3,𝔽3) | C2×#101 | semidirect |
| 121. C2×C32 | #836 | semidirect |
| 146. C32 | C2×#836 | semidirect |
| 177. C2 | #11720584 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×H(3,𝔽3) | 2 |
| C2×#88538 | 2 |
| #11720584 | 2 |
| C2×C3×#836 | 3 |