Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 286. C3 | #11865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #80741 | 2 |
| #69093 | 2 |
| #68928 | 2 |
| C3×#1350 | 2 |
| #67777 | 2 |
| #67529 | 2 |
| #67488 | 2 |
| #11865 | 3 |