Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
512 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 3. C3×#3756 | C2 | direct (N × H) |
| 5. C2×#3756 | C3 | direct (N × H) |
| 20. #3756 | C2×C3 | direct (N × H) |
| 51. C2×C33 | Q16 | semidirect |
| 77. C33 | C2×Q16 | semidirect |
| 100. C2×C32 | #216 | semidirect |
| 101. C2×C32 | C3×Q16 | semidirect |
| 123. C32 | C2×#216 | semidirect |
| 124. C32 | C2×C3×Q16 | semidirect |
| 135. C2×C3 | C3×#216 | semidirect |
| 136. C2×C3 | #3756 | direct (N × H) |
| 145. C3 | C2×C3×#216 | semidirect |
| 146. C3 | C2×#3756 | direct (N × H) |
| 147. C2 | C3×#3756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q8 | 2 |
| C2×C3×#634 | 2 |
| C3×#3756 | 2 |
| C2×C3×C3⋊(C3⋊C8) | 2 |
| C2×#3756 | 3 |
| C2×C3×#216 | 3 |