Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 187. C3 | #10687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69842 | 2 |
| #69836 | 2 |
| C3×#1275 | 2 |
| #67746 | 2 |
| #67745 | 2 |
| #10687 | 3 |