Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1108 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 1108 conjugacy classes of subgroups — too many to draw. Only its 323 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. #82523 | C2 | semidirect |
| 3. #71810 | C2 | semidirect |
| 4. #71805 | C2 | semidirect |
| 5. #71774 | C2 | semidirect |
| 218. C3 | #17773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3499 | 2 |
| #82523 | 2 |
| #71810 | 2 |
| #71805 | 2 |
| #71774 | 2 |
| #17773 | 3 |