Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
464 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 1. C3×#3237 | C2 | semidirect |
| 4. #71840 | C2 | semidirect |
| 5. #71836 | C2 | semidirect |
| 7. #67758 | C2 | semidirect |
| 35. #3237 | D3 | semidirect |
| 377. C3 | #10215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3237 | 2 |
| #83366 | 2 |
| #83358 | 2 |
| #71840 | 2 |
| #71836 | 2 |
| #70832 | 2 |
| #67758 | 2 |
| #10215 | 3 |