Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
636 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 151 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. #82015 | C2 | semidirect |
| 2. #79895 | C2 | semidirect |
| 3. C3×#2170 | C2 | semidirect |
| 4. #71456 | C2 | semidirect |
| 5. #69306 | C2 | semidirect |
| 6. #69129 | C2 | semidirect |
| 7. #69067 | C2 | semidirect |
| 8. #69066 | C2 | semidirect |
| 39. #2170 | D3 | semidirect |
| 272. C3 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82015 | 2 |
| #79895 | 2 |
| C3×#2170 | 2 |
| #71456 | 2 |
| #69306 | 2 |
| #69129 | 2 |
| #69067 | 2 |
| #69066 | 2 |
| #33860 | 3 |