Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 151 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. #82013 | C2 | semidirect |
| 2. #79894 | C2 | semidirect |
| 3. C3×#2170 | C2 | semidirect |
| 4. #71454 | C2 | semidirect |
| 5. #69305 | C2 | semidirect |
| 6. #69126 | C2 | semidirect |
| 7. #69067 | C2 | semidirect |
| 8. #69060 | C2 | semidirect |
| 11. #5752 | C22 | semidirect |
| 12. C3×#504 | C22 | semidirect |
| 14. #5142 | C22 | semidirect |
| 16. #4908 | C22 | semidirect |
| 20. C2×D48 | C22 | semidirect |
| 21. C2×D48 | C22 | semidirect |
| 24. #4700 | C22 | semidirect |
| 25. #4695 | C22 | semidirect |
| 26. C3×#364 | C22 | semidirect |
| 27. C3×#350 | C22 | semidirect |
| 28. C3×C4×C16 | C22 | semidirect |
| 29. #4516 | C22 | semidirect |
| 30. #4510 | C22 | semidirect |
| 31. #4506 | C22 | semidirect |
| 39. #2170 | D3 | semidirect |
| 67. Dic24 | D4 | semidirect |
| 69. #800 | D4 | semidirect |
| 74. D48 | D4 | semidirect |
| 84. #504 | C2×D3 | semidirect |
| 92. #364 | C2×D3 | semidirect |
| 95. #350 | C2×D3 | semidirect |
| 96. C4×C16 | C2×D3 | semidirect |
| 279. C3 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82013 | 2 |
| #79894 | 2 |
| C3×#2170 | 2 |
| #71454 | 2 |
| #69305 | 2 |
| #69126 | 2 |
| #69067 | 2 |
| #69060 | 2 |
| #33858 | 3 |