Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #70750 | C2 | semidirect |
| 5. C4×C4⋊(C3⋊C8) | C2 | semidirect |
| 6. C3×#1276 | C2 | semidirect |
| 7. #67745 | C2 | semidirect |
| 20. #4486 | C4 | semidirect |
| 21. #4485 | C4 | semidirect |
| 30. #1276 | D3 | semidirect |
| 304. C3 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #70772 | 2 |
| #70758 | 2 |
| #70750 | 2 |
| #69395 | 2 |
| C4×C4⋊(C3⋊C8) | 2 |
| C3×#1276 | 2 |
| #67745 | 2 |
| #9577 | 3 |