Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
706 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 219 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. #71362 | C2 | semidirect |
| 5. #71361 | C2 | semidirect |
| 6. #71333 | C2 | semidirect |
| 89. C2×C3×C8 | Q16 | semidirect |
| 159. C2×C8 | #216 | semidirect |
| 211. C3 | #19604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3160 | 2 |
| #83344 | 2 |
| #78442 | 2 |
| #71362 | 2 |
| #71361 | 2 |
| #71333 | 2 |
| C2×C8×C3⋊C8 | 2 |
| #19604 | 3 |