Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
698 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 129 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. C22×D48 | C2 | semidirect |
| 2. C2×#4695 | C2 | semidirect |
| 3. C2×#4509 | C2 | semidirect |
| 4. #69776 | C2 | semidirect |
| 5. C3×#1374 | C2 | semidirect |
| 25. #1374 | D3 | semidirect |
| 46. C2×D24 | D4 | semidirect |
| 51. C2×C3×C16 | D4 | semidirect |
| 136. C2×C16 | D12 | semidirect |
| 153. C2×C3×C4 | D16 | semidirect |
| 259. C2×C4 | D48 | semidirect |
| 297. C3 | #13325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D48 | 2 |
| C2×#4695 | 2 |
| C2×#4509 | 2 |
| #69776 | 2 |
| C3×#1374 | 2 |
| #13325 | 3 |