Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
803 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 803 conjugacy classes of subgroups — too many to draw. Only its 293 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. #11720520 | C2 | direct (N × H) |
| 9. C2×#6180 | C4 | semidirect |
| 20. #6180 | C2×C4 | semidirect |
| 49. C2×H(3,𝔽3) | #97 | semidirect |
| 73. H(3,𝔽3) | C2×#97 | semidirect |
| 88. C2×C32 | #803 | semidirect |
| 109. C32 | C2×#803 | semidirect |
| 131. C2 | #11720520 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×H(3,𝔽3) | 2 |
| C22×#6180 | 2 |
| #11720520 | 2 |
| C2×C3×#803 | 3 |