Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
572 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×C3×#472 | C2 | semidirect |
| 2. C22×#826 | C2 | semidirect |
| 3. #83799 | C2 | semidirect |
| 4. #72033 | C2 | semidirect |
| 5. C2×#4561 | C2 | semidirect |
| 6. C2×#4495 | C2 | semidirect |
| 7. #67729 | C2 | semidirect |
| 31. C2×#472 | D3 | semidirect |
| 49. C2×C3×D8 | D4 | semidirect |
| 71. C3×#108 | D4 | semidirect |
| 82. C2×C3⋊C16 | D4 | semidirect |
| 178. C2×D8 | #67 | semidirect |
| 201. #108 | #67 | semidirect |
| 391. C3 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#472 | 2 |
| C22×#826 | 2 |
| #83799 | 2 |
| #72033 | 2 |
| C2×#4561 | 2 |
| C2×#4495 | 2 |
| #67729 | 2 |
| #13319 | 3 |