Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
392 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. C2×#4517 | C2 | semidirect |
| 5. C2×#4503 | C2 | semidirect |
| 6. C2×#4506 | C2 | semidirect |
| 7. #67817 | C2 | semidirect |
| 320. C3 | #13394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5143 | 2 |
| C3×#2113 | 2 |
| #72016 | 2 |
| C2×#4517 | 2 |
| C2×#4503 | 2 |
| C2×#4506 | 2 |
| #67817 | 2 |
| #13394 | 3 |