Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
554 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 554 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. #83373 | C2 | semidirect |
| 4. C3×#1503 | C2 | semidirect |
| 5. #69493 | C2 | semidirect |
| 7. #67744 | C2 | semidirect |
| 37. #1503 | D3 | semidirect |
| 384. C3 | #10195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83373 | 2 |
| #83336 | 2 |
| #79305 | 2 |
| C3×#1503 | 2 |
| #69493 | 2 |
| #69487 | 2 |
| #67744 | 2 |
| #10195 | 3 |