Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
408 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 2. C2×C3×#350 | C2 | semidirect |
| 3. #72016 | C2 | semidirect |
| 4. #71439 | C2 | semidirect |
| 5. C2×#4510 | C2 | semidirect |
| 6. C2×#4505 | C2 | semidirect |
| 7. #67817 | C2 | semidirect |
| 32. C2×#350 | D3 | semidirect |
| 65. C2×C3×C16 | D4 | semidirect |
| 176. C2×C16 | #67 | semidirect |
| 359. C3 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83801 | 2 |
| C2×C3×#350 | 2 |
| #72016 | 2 |
| #71439 | 2 |
| C2×#4510 | 2 |
| C2×#4505 | 2 |
| #67817 | 2 |
| #13385 | 3 |