Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
185 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 185 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 9. #6229 | C4 | semidirect |
| 71. H(3,𝔽3) | #103 | semidirect |
| 126. C32 | #810 | semidirect |
| 127. C32 | #816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6229 | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #63566 | 3 |
| #63565 | 3 |