Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
594 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 594 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 |
|---|---|---|
| 4. #70793 | C2 | semidirect |
| 5. #70515 | C2 | semidirect |
| 6. #67737 | C2 | semidirect |
| 7. #67713 | C2 | semidirect |
| 18. #5076 | C4 | semidirect |
| 20. #5070 | C4 | semidirect |
| 58. #869 | C2×C4 | semidirect |
| 59. #869 | C2×C4 | semidirect |
| 74. C4×C3⋊C8 | C2×C4 | semidirect |
| 143. C4×Dic3 | SD16 | semidirect |
| 382. C3 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83172 | 2 |
| #83169 | 2 |
| C3×#1545 | 2 |
| #70793 | 2 |
| #70515 | 2 |
| #67737 | 2 |
| #67713 | 2 |
| #9295 | 3 |