Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 2. C3×#1992 | C2 | semidirect |
| 3. C2×#4543 | C2 | semidirect |
| 6. #69578 | C2 | semidirect |
| 7. #67659 | C2 | semidirect |
| 31. #1992 | D3 | semidirect |
| 410. C3 | #10427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83071 | 2 |
| C3×#1992 | 2 |
| C2×#4543 | 2 |
| C2×#4464 | 2 |
| #69581 | 2 |
| #69578 | 2 |
| #67659 | 2 |
| #10427 | 3 |