Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
308 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 4. #63651 | C3 | direct (N × H) |
| 60. C33 | #101 | semidirect |
| 96. C32 | #824 | semidirect |
| 97. C32 | C3×#101 | semidirect |
| 115. C3 | C3×#824 | semidirect |
| 116. C3 | #63651 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#634 | 2 |
| C33×M16 | 2 |
| C3×#3748 | 2 |
| #63651 | 3 |
| C3×#824 | 3 |