Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
458 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 93 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×#1811 | C2 | semidirect |
| 3. C2×#4553 | C2 | semidirect |
| 4. C2×#4495 | C2 | semidirect |
| 5. C2×#4495 | C2 | semidirect |
| 6. C2×#4494 | C2 | semidirect |
| 7. #67730 | C2 | semidirect |
| 31. #1811 | D3 | semidirect |
| 67. #812 | D4 | semidirect |
| 336. C3 | #13398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5135 | 2 |
| C3×#1811 | 2 |
| C2×#4553 | 2 |
| C2×#4495 | 2 |
| C2×#4494 | 2 |
| #67730 | 2 |
| #13398 | 3 |