Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
272 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 101 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. #4505 | C4 | semidirect |
| 21. #4504 | C4 | semidirect |
| 237. C3 | #13118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #71428 | 2 |
| #69829 | 2 |
| #69819 | 2 |
| C3×#1375 | 2 |
| #67819 | 2 |
| #67817 | 2 |
| #67816 | 2 |
| #13118 | 3 |