Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
840 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 263 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 |
|---|---|---|
| 1. C2×C33×Q8 | C2 | semidirect |
| 3. #88863 | C2 | semidirect |
| 4. #88862 | C2 | semidirect |
| 5. #88855 | C2 | semidirect |
| 16. C2×C32×Q8 | D3 | semidirect |
| 40. C2×C3×Q8 | C3⋊D3 | semidirect |
| 52. C33 | #137 | semidirect |
| 66. C2×Q8 | C3⋊(C3⋊D3) | semidirect |
| 76. C32 | #942 | semidirect |
| 95. C3 | #64151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q8 | 2 |
| #89076 | 2 |
| #88863 | 2 |
| #88862 | 2 |
| #88855 | 2 |
| #64151 | 3 |