Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
578 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 109 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×C3×#500 | C2 | semidirect |
| 4. #71789 | C2 | semidirect |
| 5. #71773 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 31. C2×#500 | D3 | semidirect |
| 345. C3 | #10174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#500 | 2 |
| #83215 | 2 |
| #83203 | 2 |
| #71789 | 2 |
| #71773 | 2 |
| #69735 | 2 |
| #67656 | 2 |
| #10174 | 3 |