Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
706 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 243 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 |
|---|---|---|
| 4. #68065 | C2 | semidirect |
| 5. #68064 | C2 | semidirect |
| 6. #68063 | C2 | semidirect |
| 67. C2×C3×C8 | Q16 | semidirect |
| 118. C2×C8 | Dic12 | semidirect |
| 163. C3 | #19604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78475 | 2 |
| #78442 | 2 |
| C2×C3×C82 | 2 |
| #68065 | 2 |
| #68064 | 2 |
| #68063 | 2 |
| #19604 | 3 |