Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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. #79106 | C2 | semidirect |
| 3. C2×C3×#360 | C2 | semidirect |
| 4. #72086 | C2 | semidirect |
| 5. #71450 | C2 | semidirect |
| 6. #67813 | C2 | semidirect |
| 7. #67721 | C2 | semidirect |
| 19. #5179 | C4 | semidirect |
| 20. #5147 | C4 | semidirect |
| 33. C2×#360 | D3 | semidirect |
| 43. C2×C3×Q16 | C2×C4 | semidirect |
| 45. C2×C3×D8 | C2×C4 | semidirect |
| 79. #812 | C2×C4 | semidirect |
| 168. C2×Q16 | C4×D3 | semidirect |
| 172. C2×D8 | C4×D3 | semidirect |
| 372. C3 | #13030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83894 | 2 |
| #79106 | 2 |
| C2×C3×#360 | 2 |
| #72086 | 2 |
| #71450 | 2 |
| #67813 | 2 |
| #67721 | 2 |
| #13030 | 3 |