Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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. C3×#1959 | C2 | semidirect |
| 3. C2×#4540 | C2 | semidirect |
| 4. C2×#4464 | C2 | semidirect |
| 5. #69581 | C2 | semidirect |
| 6. #69578 | C2 | semidirect |
| 7. #67659 | C2 | semidirect |
| 32. #1959 | D3 | semidirect |
| 83. #803 | D4 | semidirect |
| 465. C3 | #10424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83007 | 2 |
| C3×#1959 | 2 |
| C2×#4540 | 2 |
| C2×#4464 | 2 |
| #69581 | 2 |
| #69578 | 2 |
| #67659 | 2 |
| #10424 | 3 |