Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
364 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 364 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 |
|---|---|---|
| 1. #78479 | C2 | semidirect |
| 4. #67735 | C2 | semidirect |
| 5. #67663 | C2 | semidirect |
| 26. C2×C3×Q16 | Q8 | semidirect |
| 28. C2×C3×D8 | Q8 | semidirect |
| 95. C2×Q16 | Dic6 | semidirect |
| 97. C2×D8 | Dic6 | semidirect |
| 231. C3 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78479 | 2 |
| C3×#1975 | 2 |
| #72076 | 2 |
| #67735 | 2 |
| #67663 | 2 |
| #13373 | 3 |