Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
514 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 95 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×#5143 | C2 | semidirect |
| 3. C2×#4909 | C2 | semidirect |
| 4. C3×#2115 | C2 | semidirect |
| 5. #71448 | C2 | semidirect |
| 6. C2×#4517 | C2 | semidirect |
| 7. #67821 | C2 | semidirect |
| 37. #2115 | D3 | semidirect |
| 402. C3 | #13324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5143 | 2 |
| #83805 | 2 |
| C2×#4909 | 2 |
| C3×#2115 | 2 |
| #71448 | 2 |
| C2×#4517 | 2 |
| #67821 | 2 |
| #13324 | 3 |