Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 109 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. #83320 | C2 | semidirect |
| 3. #83169 | C2 | semidirect |
| 4. #71811 | C2 | semidirect |
| 5. #71761 | C2 | semidirect |
| 6. #69868 | C2 | semidirect |
| 7. #67668 | C2 | semidirect |
| 138. C3×M16 | SD16 | semidirect |
| 287. M16 | #214 | semidirect |
| 411. C3 | #10194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3151 | 2 |
| #83320 | 2 |
| #83169 | 2 |
| #71811 | 2 |
| #71761 | 2 |
| #69868 | 2 |
| #67668 | 2 |
| #10194 | 3 |