Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
600 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 119 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×#4926 | C2 | semidirect |
| 3. C3×#1749 | C2 | semidirect |
| 4. C2×#4464 | C2 | semidirect |
| 5. #67659 | C2 | semidirect |
| 28. #1749 | D3 | semidirect |
| 68. #803 | D4 | semidirect |
| 405. C3 | #9123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82077 | 2 |
| C2×#4926 | 2 |
| C3×#1749 | 2 |
| C2×#4464 | 2 |
| #67659 | 2 |
| #9123 | 3 |