Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
340 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 91 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. #69060 | C2 | semidirect |
| 2. #69058 | C2 | semidirect |
| 3. #68062 | C2 | semidirect |
| 4. #68058 | C2 | semidirect |
| 5. C3×#1312 | C2 | semidirect |
| 22. #1312 | D3 | semidirect |
| 101. C3×C8 | D16 | semidirect |
| 149. C8 | D48 | semidirect |
| 167. C3 | #12525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69060 | 2 |
| #69058 | 2 |
| #68062 | 2 |
| #68058 | 2 |
| C3×#1312 | 2 |
| #12525 | 3 |