Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
602 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 602 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 |
|---|---|---|
| 2. C3×#1831 | C2 | semidirect |
| 3. C2×#4481 | C2 | semidirect |
| 5. C4×C4⋊(C3⋊C8) | C2 | semidirect |
| 22. #1831 | D3 | semidirect |
| 264. C3 | #9699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #73313 | 2 |
| C3×#1831 | 2 |
| C2×#4481 | 2 |
| C2×#4485 | 2 |
| C4×C4⋊(C3⋊C8) | 2 |
| #9699 | 3 |