Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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. #71362 | C2 | semidirect |
| 5. #67802 | C2 | semidirect |
| 6. #67565 | C2 | semidirect |
| 7. #67555 | C2 | semidirect |
| 72. C3×D8 | Q16 | semidirect |
| 137. D8 | #216 | semidirect |
| 202. C3 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2226 | 2 |
| #71362 | 2 |
| #70887 | 2 |
| D8×C3⋊C8 | 2 |
| #67802 | 2 |
| #67565 | 2 |
| #67555 | 2 |
| #12447 | 3 |