Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
454 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #73397 | C2 | semidirect |
| 4. #67715 | C2 | semidirect |
| 5. #67614 | C2 | semidirect |
| 28. C3×C4⋊Q8 | Q8 | semidirect |
| 29. C3×#127 | Q8 | semidirect |
| 106. C4⋊Q8 | Dic6 | semidirect |
| 107. #127 | Dic6 | semidirect |
| 275. C3 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #73397 | 2 |
| C3×#1963 | 2 |
| #71811 | 2 |
| #67715 | 2 |
| #67614 | 2 |
| #10370 | 3 |