Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
516 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 89 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. #83374 | C2 | semidirect |
| 4. #71839 | C2 | semidirect |
| 6. #70514 | C2 | semidirect |
| 7. C3⋊#1309 | C2 | semidirect |
| 409. C3 | #10302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3254 | 2 |
| #83374 | 2 |
| #83321 | 2 |
| #71839 | 2 |
| #71815 | 2 |
| #70514 | 2 |
| C3⋊#1309 | 2 |
| #10302 | 3 |