Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 91 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. #71439 | C2 | semidirect |
| 3. C2×#4515 | C2 | semidirect |
| 4. #70721 | C2 | semidirect |
| 5. C2×#4497 | C2 | semidirect |
| 6. C2×#4490 | C2 | semidirect |
| 7. C3×#1387 | C2 | semidirect |
| 34. #1387 | D3 | semidirect |
| 73. C2×C3⋊C16 | D4 | semidirect |
| 359. C3 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79150 | 2 |
| #71439 | 2 |
| C2×#4515 | 2 |
| #70721 | 2 |
| C2×#4497 | 2 |
| C2×#4490 | 2 |
| C3×#1387 | 2 |
| #13385 | 3 |