Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
670 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 670 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 |
|---|---|---|
| 1. C2×#4699 | C2 | semidirect |
| 3. #69777 | C2 | semidirect |
| 5. C3×#1273 | C2 | semidirect |
| 23. #1273 | D3 | semidirect |
| 244. C3 | #10306 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4699 | 2 |
| C2×#4694 | 2 |
| #69777 | 2 |
| #69772 | 2 |
| C3×#1273 | 2 |
| #10306 | 3 |