Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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×#1088 | C2 | direct (N × H) |
| 5. C2×#1088 | C4 | direct (N × H) |
| 7. C2×C4×H(3,𝔽3) | C4 | semidirect |
| 8. C2×#1084 | C4 | semidirect |
| 9. C4×#272 | C4 | semidirect |
| 16. #1088 | C2×C4 | direct (N × H) |
| 17. C4×H(3,𝔽3) | C2×C4 | semidirect |
| 18. #1084 | C2×C4 | semidirect |
| 25. C2×H(3,𝔽3) | C42 | semidirect |
| 27. #272 | C42 | semidirect |
| 40. H(3,𝔽3) | C2×C42 | semidirect |
| 80. C2×C4 | #1088 | direct (N × H) |
| 95. C4 | C2×#1088 | direct (N × H) |
| 100. C2 | C4×#1088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1088 | 2 |
| C2×C4×#272 | 2 |
| C4×#1088 | 2 |
| C2×C3×C42 | 9 |