Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
636 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 351 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 |
|---|---|---|
| 4. #70685 | C2 | semidirect |
| 5. C2×#4494 | C2 | semidirect |
| 12. #5140 | C4 | semidirect |
| 41. #812 | C2×C4 | semidirect |
| 43. C2×C3⋊C16 | C2×C4 | semidirect |
| 163. C3 | #33404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2916 | 2 |
| #83784 | 2 |
| #83780 | 2 |
| #70685 | 2 |
| C2×#4494 | 2 |
| #33404 | 3 |