Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
462 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 462 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. #83874 | C2 | semidirect |
| 3. C3×#2141 | C2 | semidirect |
| 6. #67814 | C2 | semidirect |
| 7. #67725 | C2 | semidirect |
| 17. C2×#829 | C4 | semidirect |
| 20. C2×#828 | C4 | semidirect |
| 31. #2141 | D3 | semidirect |
| 329. C3 | #13034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83874 | 2 |
| C2×#5179 | 2 |
| C3×#2141 | 2 |
| #71450 | 2 |
| #70658 | 2 |
| #67814 | 2 |
| #67725 | 2 |
| #13034 | 3 |