Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
803 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 803 conjugacy classes of subgroups — too many to draw. Only its 173 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. H(3,𝔽3)×#97 | C2 | semidirect |
| 4. #11720548 | C2 | semidirect |
| 5. #11720520 | C2 | semidirect |
| 14. C8×#272 | C4 | semidirect |
| 17. C32×#97 | D3 | semidirect |
| 27. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 28. #6180 | C2×C4 | semidirect |
| 63. C32×C8 | C4×D3 | semidirect |
| 68. #272 | #97 | direct (N × H) |
| 96. #97 | #272 | direct (N × H) |
| 97. H(3,𝔽3) | C2×#97 | semidirect |
| 141. C32 | D3×#97 | semidirect |
| 150. C8 | C4×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#272 | 2 |
| C42×#272 | 2 |
| H(3,𝔽3)×#97 | 2 |
| #11720548 | 2 |
| #11720520 | 2 |
| C3×D3×#97 | 3 |