Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
690 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 690 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 |
|---|---|---|
| 1. C3×#2858 | C2 | semidirect |
| 2. #83213 | C2 | semidirect |
| 4. #71774 | C2 | semidirect |
| 5. #71759 | C2 | semidirect |
| 6. #69395 | C2 | semidirect |
| 7. #67611 | C2 | semidirect |
| 32. #2858 | D3 | semidirect |
| 372. C3 | #10281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2858 | 2 |
| #83213 | 2 |
| #83166 | 2 |
| #71774 | 2 |
| #71759 | 2 |
| #69395 | 2 |
| #67611 | 2 |
| #10281 | 3 |