Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 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. C3×#2923 | C2 | semidirect |
| 3. #71640 | C2 | semidirect |
| 4. #69853 | C2 | semidirect |
| 5. #69798 | C2 | semidirect |
| 6. #67670 | C2 | semidirect |
| 7. #67662 | C2 | semidirect |
| 33. #2923 | D3 | semidirect |
| 372. C3 | #9313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2923 | 2 |
| #82531 | 2 |
| #71640 | 2 |
| #69853 | 2 |
| #69798 | 2 |
| #67670 | 2 |
| #67662 | 2 |
| #9313 | 3 |