Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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. #71390 | C2 | semidirect |
| 4. #71384 | C2 | semidirect |
| 6. #67476 | C2 | semidirect |
| 7. #67472 | C2 | semidirect |
| 240. C3 | #12398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79415 | 2 |
| C3×#1675 | 2 |
| #71390 | 2 |
| #71384 | 2 |
| D4⋊(C3⋊C16) | 2 |
| #67476 | 2 |
| #67472 | 2 |
| #12398 | 3 |