Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
540 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#827 | C2 | semidirect |
| 3. #79184 | C2 | semidirect |
| 4. C3×#2140 | C2 | semidirect |
| 5. C2×#4517 | C2 | semidirect |
| 6. C2×#4515 | C2 | semidirect |
| 7. #67724 | C2 | semidirect |
| 34. #2140 | D3 | semidirect |
| 380. C3 | #13320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5160 | 2 |
| C22×#827 | 2 |
| #79184 | 2 |
| C3×#2140 | 2 |
| C2×#4517 | 2 |
| C2×#4515 | 2 |
| #67724 | 2 |
| #13320 | 3 |