Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
334 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 101 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. C3×Q8⋊C16 | C2 | semidirect |
| 5. #67768 | C2 | semidirect |
| 6. #67558 | C2 | semidirect |
| 7. #67506 | C2 | semidirect |
| 34. Q8⋊C16 | D3 | semidirect |
| 294. C3 | #11639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C8×Q8 | 2 |
| #69275 | 2 |
| #69052 | 2 |
| C3×Q8⋊C16 | 2 |
| #67768 | 2 |
| #67558 | 2 |
| #67506 | 2 |
| #11639 | 3 |