Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
514 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 105 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×#498 | C2 | semidirect |
| 4. #71789 | C2 | semidirect |
| 5. #71774 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 31. C2×#498 | D3 | semidirect |
| 333. C3 | #10166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#498 | 2 |
| #83215 | 2 |
| #83199 | 2 |
| #71789 | 2 |
| #71774 | 2 |
| #69735 | 2 |
| #67656 | 2 |
| #10166 | 3 |