Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1380 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
|---|---|---|
| 1. C23×D24 | C2 | semidirect |
| 2. #83742 | C2 | semidirect |
| 3. C2×#4908 | C2 | semidirect |
| 4. C3×#2112 | C2 | semidirect |
| 5. #71440 | C2 | semidirect |
| 6. #69110 | C2 | semidirect |
| 7. #69108 | C2 | semidirect |
| 12. C2×#904 | C22 | semidirect |
| 18. C2×C3×M32 | C22 | semidirect |
| 19. #5116 | C22 | semidirect |
| 20. #5115 | C22 | semidirect |
| 23. #5106 | C22 | semidirect |
| 25. C2×#800 | C22 | semidirect |
| 26. C2×D48 | C22 | semidirect |
| 27. C3×C22⋊C16 | C22 | semidirect |
| 28. #4509 | C22 | semidirect |
| 35. #2112 | D3 | semidirect |
| 56. C2×Dic12 | C23 | semidirect |
| 64. C2×D24 | D4 | semidirect |
| 66. C2×D24 | C23 | semidirect |
| 69. C2×C3×C16 | C23 | semidirect |
| 71. #818 | C23 | semidirect |
| 88. C2×M32 | C2×D3 | semidirect |
| 95. C22⋊C16 | C2×D3 | semidirect |
| 179. C2×C16 | C22×D3 | semidirect |
| 274. C22×C3 | #509 | semidirect |
| 342. C22 | #4908 | semidirect |
| 350. C3 | #33517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D24 | 2 |
| #83742 | 2 |
| C2×#4908 | 2 |
| C3×#2112 | 2 |
| #71440 | 2 |
| #69110 | 2 |
| #69108 | 2 |
| #33517 | 3 |