Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
734 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#4680 | C2 | semidirect |
| 3. #69777 | C2 | semidirect |
| 5. C3×#1273 | C2 | semidirect |
| 23. #1273 | D3 | semidirect |
| 82. C2×C3×C8 | SD16 | semidirect |
| 83. C2×C3×C8 | SD16 | semidirect |
| 168. C2×C8 | #204 | semidirect |
| 169. C2×C8 | #204 | semidirect |
| 244. C3 | #10315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4693 | 2 |
| C2×#4680 | 2 |
| #69777 | 2 |
| #69772 | 2 |
| C3×#1273 | 2 |
| #10315 | 3 |