Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
395 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 395 conjugacy classes of subgroups — too many to draw. Only its 103 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. C8×#1088 | C2 | direct (N × H) |
| 7. C2×#6188 | C4 | semidirect |
| 10. #88626 | C4 | semidirect |
| 12. C2×C8×H(3,𝔽3) | C4 | semidirect |
| 13. C2×#6180 | C4 | semidirect |
| 14. C8×#272 | C4 | semidirect |
| 18. C2×#1088 | C8 | direct (N × H) |
| 26. #6188 | C2×C4 | semidirect |
| 27. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 28. #6180 | C2×C4 | semidirect |
| 39. #1088 | C2×C8 | direct (N × H) |
| 59. C2×H(3,𝔽3) | C4×C8 | semidirect |
| 61. #272 | C4×C8 | semidirect |
| 91. H(3,𝔽3) | C2×C4×C8 | semidirect |
| 125. C2×C8 | #1088 | direct (N × H) |
| 157. C8 | C2×#1088 | direct (N × H) |
| 179. C2 | C8×#1088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1088 | 2 |
| C2×#88626 | 2 |
| C2×C8×#272 | 2 |
| C8×#1088 | 2 |
| C2×C3×C4×C8 | 9 |