Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 99 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. #79051 | C2 | semidirect |
| 3. #70521 | C2 | semidirect |
| 4. #70502 | C2 | semidirect |
| 5. #70497 | C2 | semidirect |
| 6. C3×#1309 | C2 | semidirect |
| 7. #67710 | C2 | semidirect |
| 37. #1309 | D3 | semidirect |
| 234. D12 | #100 | semidirect |
| 398. C3 | #9359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79056 | 2 |
| #79051 | 2 |
| #70521 | 2 |
| #70502 | 2 |
| #70497 | 2 |
| C3×#1309 | 2 |
| #67710 | 2 |
| #9359 | 3 |