Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
416 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 109 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. #70706 | C2 | semidirect |
| 5. #70685 | C2 | semidirect |
| 6. #67822 | C2 | semidirect |
| 7. #67813 | C2 | semidirect |
| 22. #4563 | C4 | semidirect |
| 56. #819 | C2×C4 | semidirect |
| 62. #812 | C2×C4 | semidirect |
| 269. C3 | #12953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83823 | 2 |
| C2×C3×#361 | 2 |
| C2×#4563 | 2 |
| #70706 | 2 |
| #70685 | 2 |
| #67822 | 2 |
| #67813 | 2 |
| #12953 | 3 |