Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
517 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 517 conjugacy classes of subgroups — too many to draw. Only its 146 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. C22×#1084 | C2 | semidirect |
| 3. #88552 | C2 | semidirect |
| 4. C4⋊#1084 | C2 | semidirect |
| 5. C4×#1084 | C2 | semidirect |
| 8. D4×H(3,𝔽3) | C4 | semidirect |
| 21. C22×H(3,𝔽3) | C2×C4 | semidirect |
| 23. C4×H(3,𝔽3) | C2×C4 | semidirect |
| 26. #1084 | D4 | direct (N × H) |
| 30. C32×D4 | Dic3 | semidirect |
| 52. C22×C32 | C2×Dic3 | semidirect |
| 54. C32×C4 | C2×Dic3 | semidirect |
| 59. H(3,𝔽3) | C4×D4 | semidirect |
| 99. C32 | D4×Dic3 | semidirect |
| 101. D4 | #1084 | direct (N × H) |
| 117. C22 | C2×#1084 | semidirect |
| 122. C4 | C2×#1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×H(3,𝔽3) | 2 |
| C22×#1084 | 2 |
| #88552 | 2 |
| C4⋊#1084 | 2 |
| C4×#1084 | 2 |
| C3×D4×Dic3 | 3 |