Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1382 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 331 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. C22×#836 | C2 | semidirect |
| 3. C2×#4542 | C2 | direct (N × H) |
| 14. C2×#836 | C22 | semidirect |
| 15. #4542 | C22 | direct (N × H) |
| 44. #836 | C23 | semidirect |
| 195. C22×C3 | #355 | semidirect |
| 238. C2×C3 | C2×#355 | semidirect |
| 246. C22 | #4542 | direct (N × H) |
| 255. C3 | C22×#355 | semidirect |
| 259. C2 | C2×#4542 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#124 | 2 |
| C22×#836 | 2 |
| C2×#4542 | 2 |
| C22×#355 | 3 |