Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
614 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 614 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 |
|---|---|---|
| 1. #82441 | C2 | semidirect |
| 2. C2×#5027 | C2 | semidirect |
| 4. C3×#1461 | C2 | semidirect |
| 5. #70774 | C2 | semidirect |
| 6. #70758 | C2 | semidirect |
| 7. #67745 | C2 | semidirect |
| 37. #1461 | D3 | semidirect |
| 116. C2×C3×Q8 | D8 | semidirect |
| 280. C2×Q8 | D24 | semidirect |
| 435. C3 | #10177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82441 | 2 |
| C2×#5027 | 2 |
| #79303 | 2 |
| C3×#1461 | 2 |
| #70774 | 2 |
| #70758 | 2 |
| #67745 | 2 |
| #10177 | 3 |