Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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×#2165 | C2 | semidirect |
| 3. #69849 | C2 | semidirect |
| 4. #67569 | C2 | semidirect |
| 5. #67568 | C2 | semidirect |
| 17. C3×#364 | C22 | semidirect |
| 20. #4455 | C22 | semidirect |
| 22. C8×C3⋊C8 | C22 | semidirect |
| 24. #2165 | D3 | semidirect |
| 64. #364 | C2×D3 | semidirect |
| 96. Dic12 | M16 | semidirect |
| 98. D24 | M16 | semidirect |
| 244. C3 | #11669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78541 | 2 |
| C3×#2165 | 2 |
| #69849 | 2 |
| #67569 | 2 |
| #67568 | 2 |
| #11669 | 3 |