Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
432 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 174 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. C33×Q16 | C2 | semidirect |
| 3. C32×#216 | C2 | semidirect |
| 4. C32×Dic12 | C2 | semidirect |
| 7. C3×D3×Q16 | C3 | direct (N × H) |
| 20. C32×Q16 | D3 | direct (N × H) |
| 21. C32×Q16 | C2×C3 | semidirect |
| 23. C3×#216 | C2×C3 | semidirect |
| 24. C3×Dic12 | C2×C3 | semidirect |
| 32. D3×Q16 | C32 | direct (N × H) |
| 50. C32×D3 | Q16 | direct (N × H) |
| 56. C3×Q16 | C3×D3 | direct (N × H) |
| 57. C3×Q16 | C2×C32 | semidirect |
| 59. #216 | C2×C32 | semidirect |
| 60. Dic12 | C2×C32 | semidirect |
| 75. C33 | C2×Q16 | semidirect |
| 96. C3×D3 | C3×Q16 | direct (N × H) |
| 100. Q16 | C32×D3 | direct (N × H) |
| 115. C32 | D3×Q16 | direct (N × H) |
| 116. C32 | C2×C3×Q16 | semidirect |
| 128. D3 | C32×Q16 | direct (N × H) |
| 135. C3 | C3×D3×Q16 | direct (N × H) |
| 136. C3 | C2×C32×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D3×Q8 | 2 |
| C33×Q16 | 2 |
| C32×#216 | 2 |
| C32×Dic12 | 2 |
| C32×D3×C8 | 2 |
| C2×C32×Q16 | 3 |
| C3×D3×Q16 | 3 |