Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
558 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 558 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 |
|---|---|---|
| 2. #83276 | C2 | semidirect |
| 3. C3×#1517 | C2 | semidirect |
| 4. #70774 | C2 | semidirect |
| 5. #69553 | C2 | semidirect |
| 6. #67740 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 15. #5088 | C4 | semidirect |
| 16. #5073 | C4 | semidirect |
| 32. #1517 | D3 | semidirect |
| 145. C2×C3⋊C8 | D8 | semidirect |
| 383. C3 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83302 | 2 |
| #83276 | 2 |
| C3×#1517 | 2 |
| #70774 | 2 |
| #69553 | 2 |
| #67740 | 2 |
| #67631 | 2 |
| #9293 | 3 |