Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
840 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 209 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. Q8×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. C33×Q16 | C2 | semidirect |
| 4. #88863 | C2 | semidirect |
| 5. #88862 | C2 | semidirect |
| 6. #88851 | C2 | semidirect |
| 7. #88850 | C2 | semidirect |
| 22. C32×Q16 | D3 | semidirect |
| 51. C3×Q16 | C3⋊D3 | semidirect |
| 64. C33 | #137 | semidirect |
| 82. Q16 | C3⋊(C3⋊D3) | semidirect |
| 93. C32 | #918 | semidirect |
| 115. C3 | #64127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89080 | 2 |
| Q8×C3⋊(C3⋊D3) | 2 |
| C33×Q16 | 2 |
| #88863 | 2 |
| #88862 | 2 |
| #88851 | 2 |
| #88850 | 2 |
| #64127 | 3 |