Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
252 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#4449 | C2 | semidirect |
| 2. C2×D96 | C2 | semidirect |
| 3. #69062 | C2 | semidirect |
| 4. #69060 | C2 | semidirect |
| 5. C3×#1397 | C2 | semidirect |
| 22. #1397 | D3 | semidirect |
| 39. C3×C32 | D4 | semidirect |
| 85. C32 | D12 | semidirect |
| 156. C3 | #13729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4449 | 2 |
| C2×D96 | 2 |
| #69062 | 2 |
| #69060 | 2 |
| C3×#1397 | 2 |
| #13729 | 3 |