Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
562 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#5008 | C2 | semidirect |
| 3. #79312 | C2 | semidirect |
| 4. C3×#1460 | C2 | semidirect |
| 5. #70780 | C2 | semidirect |
| 6. #70758 | C2 | semidirect |
| 7. #67745 | C2 | semidirect |
| 37. #1460 | D3 | semidirect |
| 114. C2×C3×D4 | SD16 | semidirect |
| 273. C2×D4 | #204 | semidirect |
| 411. C3 | #10180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82307 | 2 |
| C2×#5008 | 2 |
| #79312 | 2 |
| C3×#1460 | 2 |
| #70780 | 2 |
| #70758 | 2 |
| #67745 | 2 |
| #10180 | 3 |