Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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×#5195 | C2 | semidirect |
| 3. C2×#4896 | C2 | semidirect |
| 4. C2×C3×#359 | C2 | semidirect |
| 5. C2×#4503 | C2 | semidirect |
| 6. C2×#4508 | C2 | semidirect |
| 7. #67732 | C2 | semidirect |
| 35. C2×#359 | D3 | semidirect |
| 66. C2×Dic12 | D4 | semidirect |
| 78. C3×#108 | D4 | semidirect |
| 87. #812 | D4 | semidirect |
| 217. #108 | #67 | semidirect |
| 415. C3 | #13308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83917 | 2 |
| C2×#5195 | 2 |
| C2×#4896 | 2 |
| C2×C3×#359 | 2 |
| C2×#4503 | 2 |
| C2×#4508 | 2 |
| #67732 | 2 |
| #13308 | 3 |