Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 111 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. #70792 | C2 | semidirect |
| 5. #70741 | C2 | semidirect |
| 6. #69493 | C2 | semidirect |
| 7. C4×#807 | C2 | semidirect |
| 14. #5093 | C4 | semidirect |
| 15. #5080 | C4 | semidirect |
| 16. #5076 | C4 | semidirect |
| 17. #5070 | C4 | semidirect |
| 239. C3⋊C8 | #104 | semidirect |
| 374. C3 | #9722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83290 | 2 |
| C3×#1502 | 2 |
| #71818 | 2 |
| #70792 | 2 |
| #70741 | 2 |
| #69493 | 2 |
| C4×#807 | 2 |
| #9722 | 3 |