Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 2. C2×C3×#360 | C2 | semidirect |
| 3. #72078 | C2 | semidirect |
| 4. #71439 | C2 | semidirect |
| 5. #70562 | C2 | semidirect |
| 6. C2×#4488 | C2 | semidirect |
| 7. #67812 | C2 | semidirect |
| 32. C2×#360 | D3 | semidirect |
| 77. C3×#106 | D4 | semidirect |
| 215. #106 | #67 | semidirect |
| 419. C3 | #13410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83904 | 2 |
| C2×C3×#360 | 2 |
| #72078 | 2 |
| #71439 | 2 |
| #70562 | 2 |
| C2×#4488 | 2 |
| #67812 | 2 |
| #13410 | 3 |