Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
368 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 107 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×#1566 | C2 | semidirect |
| 3. C4×#812 | C2 | semidirect |
| 4. #67465 | C2 | semidirect |
| 23. #1566 | D3 | semidirect |
| 235. C3 | #11680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78470 | 2 |
| C3×#1566 | 2 |
| C4×#812 | 2 |
| #67465 | 2 |
| #11680 | 3 |