Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
236 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 71 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. #71312 | C2 | semidirect |
| 5. #67793 | C2 | semidirect |
| 6. #67474 | C2 | semidirect |
| 7. #67469 | C2 | semidirect |
| 123. C3×D4 | Q32 | semidirect |
| 185. D4 | #829 | semidirect |
| 216. C3 | #12431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1669 | 2 |
| #71312 | 2 |
| D4×C3⋊C16 | 2 |
| #70850 | 2 |
| #67793 | 2 |
| #67474 | 2 |
| #67469 | 2 |
| #12431 | 3 |