Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
642 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. C3×#3152 | C2 | semidirect |
| 3. C2×#5088 | C2 | semidirect |
| 4. #71802 | C2 | semidirect |
| 5. #71773 | C2 | semidirect |
| 6. #69876 | C2 | semidirect |
| 7. #67667 | C2 | semidirect |
| 31. #3152 | D3 | semidirect |
| 131. C3×M16 | D8 | semidirect |
| 266. M16 | #213 | semidirect |
| 370. C3 | #10168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3152 | 2 |
| #83302 | 2 |
| C2×#5088 | 2 |
| #71802 | 2 |
| #71773 | 2 |
| #69876 | 2 |
| #67667 | 2 |
| #10168 | 3 |