Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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×#3165 | C2 | semidirect |
| 4. #71825 | C2 | semidirect |
| 5. #71789 | C2 | semidirect |
| 7. #67669 | C2 | semidirect |
| 34. #3165 | D3 | semidirect |
| 353. C3 | #10116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3165 | 2 |
| #83366 | 2 |
| #83216 | 2 |
| #71825 | 2 |
| #71789 | 2 |
| #69859 | 2 |
| #67669 | 2 |
| #10116 | 3 |