Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2062 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 331 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. C22×#834 | C2 | semidirect |
| 3. C2×#4545 | C2 | direct (N × H) |
| 6. C23×C3×D4 | C4 | semidirect |
| 9. C2×C3×#127 | C4 | semidirect |
| 11. C22×C3×C42 | C4 | semidirect |
| 14. C2×#834 | C22 | semidirect |
| 15. #4545 | C22 | direct (N × H) |
| 30. C22×C3×D4 | C2×C4 | semidirect |
| 38. C3×#127 | C2×C4 | semidirect |
| 41. C2×C3×C42 | C2×C4 | semidirect |
| 45. #834 | C23 | semidirect |
| 47. C23×D4 | Dic3 | semidirect |
| 50. C2×#127 | Dic3 | semidirect |
| 53. C22×C42 | Dic3 | semidirect |
| 84. C2×C3×D4 | C22×C4 | semidirect |
| 96. C3×C42 | C22×C4 | semidirect |
| 110. C22×D4 | C2×Dic3 | semidirect |
| 118. #127 | C2×Dic3 | semidirect |
| 123. C2×C42 | C2×Dic3 | semidirect |
| 191. C2×D4 | C22×Dic3 | semidirect |
| 205. C42 | C22×Dic3 | semidirect |
| 220. C22×C3 | #353 | semidirect |
| 271. C2×C3 | C2×#353 | semidirect |
| 287. C22 | #4545 | direct (N × H) |
| 295. C3 | C22×#353 | semidirect |
| 301. C2 | C2×#4545 | 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 |
| C22×#834 | 2 |
| C2×#4545 | 2 |
| C22×#353 | 3 |