Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
294 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 20. #4511 | C4 | semidirect |
| 243. C3 | #13180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #71428 | 2 |
| C2×#4511 | 2 |
| #70702 | 2 |
| #70607 | 2 |
| #70596 | 2 |
| C3×#1387 | 2 |
| #67732 | 2 |
| #13180 | 3 |