Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
638 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 153 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×#4680 | C2 | semidirect |
| 4. #69771 | C2 | semidirect |
| 5. C3×#1273 | C2 | semidirect |
| 23. #1273 | D3 | semidirect |
| 240. C3 | #10312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4694 | 2 |
| C2×#4680 | 2 |
| #69772 | 2 |
| #69771 | 2 |
| C3×#1273 | 2 |
| #10312 | 3 |