Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
246 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 85. C3×C16 | Q16 | semidirect |
| 86. C3⋊C16 | Q16 | semidirect |
| 142. C16 | #216 | semidirect |
| 179. C3 | #12524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2252 | 2 |
| #71385 | 2 |
| #71384 | 2 |
| #71362 | 2 |
| #71361 | 2 |
| #69046 | 2 |
| #67498 | 2 |
| #12524 | 3 |