Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
452 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #70836 | C2 | semidirect |
| 5. #69862 | C2 | semidirect |
| 6. #67754 | C2 | semidirect |
| 7. #67665 | C2 | semidirect |
| 20. #5031 | C4 | semidirect |
| 22. #5021 | C4 | semidirect |
| 23. #5019 | C4 | semidirect |
| 25. #5008 | C4 | semidirect |
| 383. C3 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2970 | 2 |
| #82535 | 2 |
| #71643 | 2 |
| #70836 | 2 |
| #69862 | 2 |
| #67754 | 2 |
| #67665 | 2 |
| #9159 | 3 |