Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. C2×#4513 | C2 | semidirect |
| 5. #70650 | C2 | semidirect |
| 6. C3×#1384 | C2 | semidirect |
| 7. #67726 | C2 | semidirect |
| 24. #4508 | C4 | semidirect |
| 33. #1384 | D3 | semidirect |
| 54. C2×C3×C16 | C2×C4 | semidirect |
| 65. #812 | C2×C4 | semidirect |
| 152. C2×C16 | C4×D3 | semidirect |
| 299. C3 | #12934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79178 | 2 |
| #71437 | 2 |
| C2×#4513 | 2 |
| #70665 | 2 |
| #70650 | 2 |
| C3×#1384 | 2 |
| #67726 | 2 |
| #12934 | 3 |