Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1502 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1502 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 |
|---|---|---|
| 3. C2×#4541 | C2 | direct (N × H) |
| 5. C23×C3×Q8 | C4 | semidirect |
| 8. C2×C3×#124 | C4 | semidirect |
| 11. C22×C3×C42 | C4 | semidirect |
| 15. #4541 | C22 | direct (N × H) |
| 23. C22×C3×Q8 | C2×C4 | semidirect |
| 35. C3×#124 | C2×C4 | semidirect |
| 40. C2×C3×C42 | C2×C4 | semidirect |
| 45. C23×Q8 | Dic3 | semidirect |
| 48. C2×#124 | Dic3 | semidirect |
| 52. C22×C42 | Dic3 | semidirect |
| 67. C2×C3×Q8 | C22×C4 | semidirect |
| 92. C3×C42 | C22×C4 | semidirect |
| 99. C22×Q8 | C2×Dic3 | semidirect |
| 111. #124 | C2×Dic3 | semidirect |
| 118. C2×C42 | C2×Dic3 | semidirect |
| 165. C2×Q8 | C22×Dic3 | semidirect |
| 192. C42 | C22×Dic3 | semidirect |
| 203. C22×C3 | #354 | semidirect |
| 249. C2×C3 | C2×#354 | semidirect |
| 261. C22 | #4541 | direct (N × H) |
| 270. C3 | C22×#354 | semidirect |
| 275. C2 | C2×#4541 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#124 | 2 |
| C22×#834 | 2 |
| C2×#4541 | 2 |
| C22×#354 | 3 |