Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
3798 conjugacy classes of subgroups; only the 1179 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 1179 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×#5220 | C2 | semidirect |
| 3. #83174 | C2 | direct (N × H) |
| 4. C2×#4937 | C2 | semidirect |
| 8. C2×C3×#127 | C4 | semidirect |
| 12. #5220 | C22 | semidirect |
| 14. #4937 | C22 | semidirect |
| 22. C22×C3×D4 | C2×C4 | semidirect |
| 28. C3×#127 | C2×C4 | semidirect |
| 29. C2×C3×C42 | C2×C4 | semidirect |
| 36. C2×#127 | Dic3 | semidirect |
| 51. C2×C3×D4 | C22×C4 | semidirect |
| 59. C3×C42 | C22×C4 | semidirect |
| 64. C22×D4 | C2×Dic3 | semidirect |
| 70. #127 | C2×Dic3 | semidirect |
| 73. C2×C42 | C2×Dic3 | semidirect |
| 100. C2×D4 | C22×Dic3 | semidirect |
| 109. C42 | C22×Dic3 | semidirect |
| 137. C2×C3 | #2380 | semidirect |
| 150. C3 | C2×#2380 | semidirect |
| 152. C2 | #83174 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#127 | 2 |
| C2×#5220 | 2 |
| #83174 | 2 |
| C2×#4937 | 2 |
| C2×#2380 | 3 |