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. #71427 | C2 | semidirect |
| 5. C2×#4487 | C2 | semidirect |
| 6. C3×#1386 | C2 | semidirect |
| 7. #67725 | C2 | semidirect |
| 23. #4515 | C4 | semidirect |
| 32. #1386 | D3 | semidirect |
| 53. C3×M32 | C2×C4 | semidirect |
| 66. C2×C3⋊C16 | C2×C4 | semidirect |
| 150. M32 | 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 |
|---|---|
| #79116 | 2 |
| #71438 | 2 |
| #71427 | 2 |
| #70665 | 2 |
| C2×#4487 | 2 |
| C3×#1386 | 2 |
| #67725 | 2 |
| #12934 | 3 |