Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
328 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 93 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. D3×C4⋊C16 | C2 | semidirect |
| 3. #69073 | C2 | semidirect |
| 4. C3×#1338 | C2 | semidirect |
| 5. #67769 | C2 | semidirect |
| 6. #67557 | C2 | semidirect |
| 7. #67515 | C2 | semidirect |
| 32. #1338 | D3 | semidirect |
| 299. C3 | #11626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79938 | 2 |
| D3×C4⋊C16 | 2 |
| #69073 | 2 |
| C3×#1338 | 2 |
| #67769 | 2 |
| #67557 | 2 |
| #67515 | 2 |
| #11626 | 3 |