Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 1. C3×#2246 | C2 | semidirect |
| 2. #71291 | C2 | semidirect |
| 3. #71290 | C2 | semidirect |
| 4. #71276 | C2 | semidirect |
| 5. #71275 | C2 | semidirect |
| 6. #69061 | C2 | semidirect |
| 7. #67498 | C2 | semidirect |
| 25. #2246 | D3 | semidirect |
| 85. C3×C16 | D8 | semidirect |
| 86. C3⋊C16 | D8 | semidirect |
| 151. C16 | #213 | semidirect |
| 199. C3 | #12519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2246 | 2 |
| #71291 | 2 |
| #71290 | 2 |
| #71276 | 2 |
| #71275 | 2 |
| #69061 | 2 |
| #67498 | 2 |
| #12519 | 3 |