Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
466 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 127 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. C3×#3407 | C2 | semidirect |
| 3. #72014 | C2 | semidirect |
| 4. #71448 | C2 | semidirect |
| 5. #67816 | C2 | semidirect |
| 22. #3407 | D3 | semidirect |
| 51. C2×C3×C16 | D4 | semidirect |
| 136. C2×C16 | #67 | semidirect |
| 271. C3 | #13076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3407 | 2 |
| #83800 | 2 |
| #72014 | 2 |
| #71448 | 2 |
| #67816 | 2 |
| #13076 | 3 |