Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #69828 | C2 | semidirect |
| 5. #69555 | C2 | semidirect |
| 6. C3×#1295 | C2 | semidirect |
| 7. #67659 | C2 | semidirect |
| 21. #4715 | C4 | semidirect |
| 37. #1295 | D3 | semidirect |
| 72. #869 | C2×C4 | semidirect |
| 76. C3×#97 | C2×C4 | semidirect |
| 206. #97 | C4×D3 | semidirect |
| 432. C3 | #9003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4715 | 2 |
| #74230 | 2 |
| #69828 | 2 |
| C2×#4464 | 2 |
| #69555 | 2 |
| C3×#1295 | 2 |
| #67659 | 2 |
| #9003 | 3 |