Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
347 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 347 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #11720256 | C2 | direct (N × H) |
| 99. C2×H(3,𝔽3) | Q32 | semidirect |
| 147. H(3,𝔽3) | C2×Q32 | semidirect |
| 183. C2×C32 | Dic24 | semidirect |
| 184. C2×C32 | #829 | semidirect |
| 215. C32 | C2×Dic24 | semidirect |
| 216. C32 | C2×#829 | semidirect |
| 243. C2 | #11720256 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88530 | 2 |
| C2×#3746⋊C3 | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| #11720256 | 2 |
| C2×#63551 | 3 |
| C2×#63550 | 3 |