Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
632 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 113 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. #83172 | C2 | semidirect |
| 3. C3×#1545 | C2 | semidirect |
| 4. #70790 | C2 | semidirect |
| 5. #70513 | C2 | semidirect |
| 6. #67737 | C2 | semidirect |
| 7. #67713 | C2 | semidirect |
| 20. #5073 | C4 | semidirect |
| 22. #5070 | C4 | semidirect |
| 31. #1545 | D3 | semidirect |
| 58. #874 | C2×C4 | semidirect |
| 61. #869 | C2×C4 | semidirect |
| 76. C4×C3⋊C8 | C2×C4 | semidirect |
| 149. C4×Dic3 | D8 | semidirect |
| 415. C3 | #9299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83172 | 2 |
| #83166 | 2 |
| C3×#1545 | 2 |
| #70790 | 2 |
| #70513 | 2 |
| #67737 | 2 |
| #67713 | 2 |
| #9299 | 3 |