Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
787 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 787 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C2×C22⋊#1088 | C2 | semidirect |
| 3. #11720780 | C2 | direct (N × H) |
| 4. C23×#272 | C4 | semidirect |
| 7. C22×C4×H(3,𝔽3) | C4 | semidirect |
| 10. C2×C4⋊#272 | C4 | semidirect |
| 13. C22⋊#1088 | C22 | semidirect |
| 21. C22×#272 | C2×C4 | semidirect |
| 29. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 78. C2×H(3,𝔽3) | #99 | semidirect |
| 118. H(3,𝔽3) | C2×#99 | semidirect |
| 165. C22×C4 | #1088 | semidirect |
| 216. C2×C4 | C2×#1088 | semidirect |
| 254. C2 | #11720780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#272 | 2 |
| C2×C22⋊#1088 | 2 |
| #11720780 | 2 |
| C2×C3×#99 | 9 |