Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
500 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 81 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. #83316 | C2 | semidirect |
| 3. #83315 | C2 | semidirect |
| 4. #71803 | C2 | semidirect |
| 5. #71799 | C2 | semidirect |
| 6. #70830 | C2 | semidirect |
| 7. #67757 | C2 | semidirect |
| 386. C3 | #10040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3214 | 2 |
| #83316 | 2 |
| #83315 | 2 |
| #71803 | 2 |
| #71799 | 2 |
| #70830 | 2 |
| #67757 | 2 |
| #10040 | 3 |