Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2248 | C2 | semidirect |
| 2. #71313 | C2 | semidirect |
| 3. #71298 | C2 | semidirect |
| 4. #71291 | C2 | semidirect |
| 6. #69061 | C2 | semidirect |
| 7. C16×C3⋊C8 | C2 | semidirect |
| 25. #2248 | D3 | semidirect |
| 85. C3×C16 | D8 | semidirect |
| 86. C3⋊C16 | D8 | semidirect |
| 127. C3⋊C8 | SD32 | semidirect |
| 150. C16 | #213 | semidirect |
| 194. C3 | #12517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2248 | 2 |
| #71313 | 2 |
| #71298 | 2 |
| #71291 | 2 |
| #71276 | 2 |
| #69061 | 2 |
| C16×C3⋊C8 | 2 |
| #12517 | 3 |