Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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. #73770 | C2 | semidirect |
| 3. #70790 | C2 | semidirect |
| 4. #70757 | C2 | semidirect |
| 5. #69469 | C2 | semidirect |
| 6. C3×#1303 | C2 | semidirect |
| 7. #67713 | C2 | semidirect |
| 22. #4843 | C4 | semidirect |
| 23. #4841 | C4 | semidirect |
| 35. #1303 | D3 | semidirect |
| 57. #874 | C2×C4 | semidirect |
| 66. #869 | C2×C4 | semidirect |
| 69. C3×C4⋊C8 | C2×C4 | semidirect |
| 192. C4⋊C8 | C4×D3 | semidirect |
| 421. C3 | #9179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79055 | 2 |
| #73770 | 2 |
| #70790 | 2 |
| #70757 | 2 |
| #69469 | 2 |
| C3×#1303 | 2 |
| #67713 | 2 |
| #9179 | 3 |