Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. #79320 | C2 | semidirect |
| 5. #70831 | C2 | semidirect |
| 6. #70813 | C2 | semidirect |
| 7. #67751 | C2 | semidirect |
| 341. C3 | #10131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83169 | 2 |
| C2×#5071 | 2 |
| #79320 | 2 |
| C3×#1555 | 2 |
| #70831 | 2 |
| #70813 | 2 |
| #67751 | 2 |
| #10131 | 3 |