Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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×#2247 | C2 | semidirect |
| 4. #67826 | C2 | semidirect |
| 5. C4⋊(C3⋊C32) | C2 | semidirect |
| 18. #2247 | D3 | semidirect |
| 120. C3×C4 | SD64 | semidirect |
| 149. C4 | #4521 | semidirect |
| 152. C3 | #13687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2247 | 2 |
| C2×#4521 | 2 |
| C4×D48 | 2 |
| #67826 | 2 |
| C4⋊(C3⋊C32) | 2 |
| #13687 | 3 |