Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. C2×#4517 | C2 | semidirect |
| 5. #71445 | C2 | semidirect |
| 6. #71427 | C2 | semidirect |
| 7. #67818 | C2 | semidirect |
| 313. C3 | #13397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83807 | 2 |
| C3×#2117 | 2 |
| #72013 | 2 |
| C2×#4517 | 2 |
| #71445 | 2 |
| #71427 | 2 |
| #67818 | 2 |
| #13397 | 3 |