Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
330 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 99 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. #69066 | C2 | semidirect |
| 2. #69061 | C2 | semidirect |
| 4. #68060 | C2 | semidirect |
| 5. C3×C8×C16 | C2 | semidirect |
| 20. C8×C16 | D3 | semidirect |
| 127. C3 | #12518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69066 | 2 |
| #69061 | 2 |
| #69060 | 2 |
| #68060 | 2 |
| C3×C8×C16 | 2 |
| #12518 | 3 |