Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
398 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. C3×#1518 | C2 | semidirect |
| 3. #71828 | C2 | semidirect |
| 5. #70749 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 32. #1518 | D3 | semidirect |
| 338. C3 | #10468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83350 | 2 |
| C3×#1518 | 2 |
| #71828 | 2 |
| #70783 | 2 |
| #70749 | 2 |
| #69556 | 2 |
| #67631 | 2 |
| #10468 | 3 |