Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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. #83314 | C2 | semidirect |
| 3. #71802 | C2 | semidirect |
| 4. #70472 | C2 | semidirect |
| 5. #67705 | C2 | semidirect |
| 91. C2×Dic6 | D8 | semidirect |
| 292. C3 | #10255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3245 | 2 |
| #83314 | 2 |
| #71802 | 2 |
| #70472 | 2 |
| #67705 | 2 |
| #10255 | 3 |