Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
307 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. C22×#322 | C3 | semidirect |
| 16. C8×A4 | C8 | semidirect |
| 31. #322 | A4 | direct (N × H) |
| 47. C22×C8 | C3×C8 | semidirect |
| 91. A4 | #322 | direct (N × H) |
| 114. C8 | C8×A4 | semidirect |
| 124. C22 | C3×#322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×A4 | 2 |
| C22×#322 | 3 |
| C3×#322 | 4 |