Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
671 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 671 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4×#6229 | C2 | semidirect |
| 4. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 6. #11720550 | C2 | semidirect |
| 7. #11720549 | C2 | semidirect |
| 20. #88528 | C4 | direct (N × H) |
| 24. C32×C4×C8 | D3 | semidirect |
| 39. #6229 | C2×C4 | semidirect |
| 41. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 61. C4×H(3,𝔽3) | SD16 | semidirect |
| 94. C32×C8 | C4×D3 | semidirect |
| 129. C32×C4 | #204 | semidirect |
| 141. C4×C8 | #272 | semidirect |
| 142. H(3,𝔽3) | C4×SD16 | semidirect |
| 209. C32 | C4×#204 | semidirect |
| 223. C8 | C4×#272 | semidirect |
| 240. C4 | #88528 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88528 | 2 |
| C4×C4⋊#272 | 2 |
| C4×#6229 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #11720554 | 2 |
| #11720550 | 2 |
| #11720549 | 2 |
| C3×C4×#204 | 3 |