Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
226 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 67 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. #88945 | C2 | direct (N × H) |
| 8. C2×C3⋊#157 | C4 | semidirect |
| 23. C3⋊#157 | C2×C4 | semidirect |
| 34. C2×C33 | C4⋊C4 | semidirect |
| 36. C3×C3⋊D3 | C4⋊C4 | semidirect |
| 58. C33 | C2×C4⋊C4 | semidirect |
| 71. C2×C32 | Dic3⋊C4 | semidirect |
| 73. C3⋊D3 | Dic3⋊C4 | semidirect |
| 99. C32 | C2×Dic3⋊C4 | semidirect |
| 114. C2×C3 | #3777 | semidirect |
| 129. C3 | C2×#3777 | semidirect |
| 133. C2 | #88945 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊#157 | 2 |
| C22×C3×#157 | 2 |
| #88945 | 2 |
| C2×#3777 | 3 |
| C2×Dic3⋊C4 | 9 |