Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
422 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 422 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. C2×#4563 | C2 | semidirect |
| 3. #72033 | C2 | semidirect |
| 4. #72013 | C2 | semidirect |
| 5. #72006 | C2 | semidirect |
| 6. #70650 | C2 | semidirect |
| 7. #67725 | C2 | semidirect |
| 69. C2×C3⋊C16 | D4 | semidirect |
| 324. C3 | #13396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3058 | 2 |
| C2×#4563 | 2 |
| #72033 | 2 |
| #72013 | 2 |
| #72006 | 2 |
| #70650 | 2 |
| #67725 | 2 |
| #13396 | 3 |