Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
249 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 44 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 |
|---|---|---|
| 1. C22×#1088 | C2 | semidirect |
| 3. C22⋊#1088 | C2 | semidirect |
| 4. C4⋊#1088 | C2 | semidirect |
| 5. C4×#1088 | C2 | semidirect |
| 11. D4×H(3,𝔽3) | C4 | semidirect |
| 12. #6235 | C4 | semidirect |
| 13. C4⋊#272 | C4 | semidirect |
| 16. C22×H(3,𝔽3) | C2×C4 | semidirect |
| 19. C2×#272 | C2×C4 | semidirect |
| 23. #1088 | D4 | direct (N × H) |
| 24. C4×H(3,𝔽3) | C2×C4 | semidirect |
| 25. #1084 | C2×C4 | semidirect |
| 51. H(3,𝔽3) | C4×D4 | semidirect |
| 97. D4 | #1088 | direct (N × H) |
| 117. C22 | C2×#1088 | semidirect |
| 122. C4 | C2×#1088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1088 | 2 |
| D4×#272 | 2 |
| C22⋊#1088 | 2 |
| C4⋊#1088 | 2 |
| C4×#1088 | 2 |
| C3×C4×D4 | 9 |