Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
578 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#5078 | C2 | semidirect |
| 4. C3×#1966 | C2 | semidirect |
| 5. #70506 | C2 | semidirect |
| 7. #67667 | C2 | semidirect |
| 33. #1966 | D3 | semidirect |
| 345. C3 | #10174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83215 | 2 |
| C2×#5078 | 2 |
| #78538 | 2 |
| C3×#1966 | 2 |
| #70506 | 2 |
| #70498 | 2 |
| #67667 | 2 |
| #10174 | 3 |