Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
508 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 109 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×#4717 | C2 | semidirect |
| 3. C2×#4518 | C2 | semidirect |
| 4. C2×#4516 | C2 | semidirect |
| 5. #69825 | C2 | semidirect |
| 6. C3×#1375 | C2 | semidirect |
| 7. #67816 | C2 | semidirect |
| 22. C2×#800 | C4 | semidirect |
| 23. C2×D48 | C4 | semidirect |
| 34. #1375 | D3 | semidirect |
| 131. Dic12 | C22⋊C4 | semidirect |
| 137. D24 | C22⋊C4 | semidirect |
| 348. C3 | #13040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4908 | 2 |
| C2×#4717 | 2 |
| C2×#4518 | 2 |
| C2×#4516 | 2 |
| #69825 | 2 |
| C3×#1375 | 2 |
| #67816 | 2 |
| #13040 | 3 |