Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
967 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 967 conjugacy classes of subgroups — too many to draw. Only its 143 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. #11720787 | C2 | direct (N × H) |
| 7. C22×#1088 | C4 | semidirect |
| 9. C22×C4×H(3,𝔽3) | C4 | semidirect |
| 10. C22×#1084 | C4 | semidirect |
| 12. C2×C4×#272 | C4 | semidirect |
| 25. C2×#1088 | C2×C4 | semidirect |
| 27. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 29. C2×#1084 | C2×C4 | semidirect |
| 73. C2×H(3,𝔽3) | #95 | semidirect |
| 77. #272 | #95 | semidirect |
| 114. H(3,𝔽3) | C2×#95 | semidirect |
| 161. C22×C4 | #1088 | semidirect |
| 210. C2×C4 | C2×#1088 | semidirect |
| 246. C2 | #11720787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1088 | 2 |
| C22×C4×#272 | 2 |
| #11720787 | 2 |
| C2×C3×#95 | 9 |