Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 1. #83823 | C2 | semidirect |
| 3. C3×#2140 | C2 | semidirect |
| 4. #71450 | C2 | semidirect |
| 5. #70658 | C2 | semidirect |
| 6. #67814 | C2 | semidirect |
| 7. #67725 | C2 | semidirect |
| 17. C2×#827 | C4 | semidirect |
| 20. C2×#826 | C4 | semidirect |
| 31. #2140 | D3 | semidirect |
| 51. C2×Dic12 | C2×C4 | semidirect |
| 56. C2×D24 | C2×C4 | semidirect |
| 72. C2×C3⋊C16 | C2×C4 | semidirect |
| 340. C3 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83823 | 2 |
| C2×#5147 | 2 |
| C3×#2140 | 2 |
| #71450 | 2 |
| #70658 | 2 |
| #67814 | 2 |
| #67725 | 2 |
| #13033 | 3 |