Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
310 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 73 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. C3×#1676 | C2 | semidirect |
| 4. #71385 | C2 | semidirect |
| 5. #67768 | C2 | semidirect |
| 6. #67475 | C2 | semidirect |
| 29. #1676 | D3 | semidirect |
| 244. C3 | #12408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D24 | 2 |
| C3×#1676 | 2 |
| #71388 | 2 |
| #71385 | 2 |
| #67768 | 2 |
| #67475 | 2 |
| #67471 | 2 |
| #12408 | 3 |