Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
648 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#5055 | C2 | semidirect |
| 3. C2×#4715 | C2 | semidirect |
| 4. C2×C3×#329 | C2 | semidirect |
| 5. #69828 | C2 | semidirect |
| 6. C2×#4464 | C2 | semidirect |
| 7. #67659 | C2 | semidirect |
| 37. C2×#329 | D3 | semidirect |
| 73. #869 | D4 | semidirect |
| 77. C3×#97 | D4 | semidirect |
| 84. #803 | D4 | semidirect |
| 206. #97 | #67 | semidirect |
| 413. C3 | #10081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83007 | 2 |
| C2×#5055 | 2 |
| C2×#4715 | 2 |
| C2×C3×#329 | 2 |
| #69828 | 2 |
| C2×#4464 | 2 |
| #67659 | 2 |
| #10081 | 3 |