Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
376 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 4. #67822 | C2 | semidirect |
| 5. #67816 | C2 | semidirect |
| 230. C3 | #12874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83784 | 2 |
| C3×#2115 | 2 |
| #72014 | 2 |
| #67822 | 2 |
| #67816 | 2 |
| #12874 | 3 |