Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
490 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #83780 | C2 | semidirect |
| 3. C3×#1812 | C2 | semidirect |
| 4. #70652 | C2 | semidirect |
| 5. #67725 | C2 | semidirect |
| 13. #5135 | C4 | semidirect |
| 24. #1812 | D3 | semidirect |
| 54. C2×C3⋊C16 | D4 | semidirect |
| 247. C3 | #13074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83799 | 2 |
| #83780 | 2 |
| C3×#1812 | 2 |
| #70652 | 2 |
| #67725 | 2 |
| #13074 | 3 |