Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
552 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. #83222 | C2 | semidirect |
| 4. C3×#1997 | C2 | semidirect |
| 5. #69862 | C2 | semidirect |
| 7. #67710 | C2 | semidirect |
| 35. #1997 | D3 | semidirect |
| 355. C3 | #10107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83222 | 2 |
| #83203 | 2 |
| #79065 | 2 |
| C3×#1997 | 2 |
| #69862 | 2 |
| #69853 | 2 |
| #67710 | 2 |
| #10107 | 3 |