Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. #78577 | C2 | semidirect |
| 4. #70928 | C2 | semidirect |
| 5. #70927 | C2 | semidirect |
| 6. #70920 | C2 | semidirect |
| 7. #70724 | C2 | semidirect |
| 8. #69886 | C2 | semidirect |
| 23. #4716 | C22 | semidirect |
| 25. #4699 | C22 | semidirect |
| 27. #4683 | C22 | semidirect |
| 30. #4496 | C22 | semidirect |
| 31. #4494 | C22 | semidirect |
| 32. #4466 | C22 | semidirect |
| 33. #4463 | C22 | semidirect |
| 316. C3 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2955 | 2 |
| #78577 | 2 |
| #72113 | 2 |
| #70928 | 2 |
| #70927 | 2 |
| #70920 | 2 |
| #70724 | 2 |
| #69886 | 2 |
| #33693 | 3 |