Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
486 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 131 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. #83780 | C2 | semidirect |
| 3. C2×#4563 | C2 | semidirect |
| 4. #72014 | C2 | semidirect |
| 5. #67727 | C2 | semidirect |
| 53. #812 | D4 | semidirect |
| 247. C3 | #13079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3058 | 2 |
| #83780 | 2 |
| C2×#4563 | 2 |
| #72014 | 2 |
| #67727 | 2 |
| #13079 | 3 |