Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
380 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 22. #4565 | C4 | semidirect |
| 258. C3 | #12954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83874 | 2 |
| C2×C3×#362 | 2 |
| C2×#4565 | 2 |
| #70706 | 2 |
| #70685 | 2 |
| #67822 | 2 |
| #67813 | 2 |
| #12954 | 3 |