Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
226 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 69 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. C3×#1594 | C2 | semidirect |
| 3. #68083 | C2 | semidirect |
| 4. #67762 | C2 | semidirect |
| 5. #67465 | C2 | semidirect |
| 6. #67464 | C2 | semidirect |
| 7. #67442 | C2 | semidirect |
| 26. #1594 | D3 | semidirect |
| 90. C3⋊C16 | M16 | semidirect |
| 211. C3 | #12089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1594 | 2 |
| #70885 | 2 |
| #68083 | 2 |
| #67762 | 2 |
| #67465 | 2 |
| #67464 | 2 |
| #67442 | 2 |
| #12089 | 3 |