Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
508 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 508 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. #79287 | C2 | semidirect |
| 3. #70789 | C2 | semidirect |
| 4. #69812 | C2 | semidirect |
| 5. #69798 | C2 | semidirect |
| 6. C3×#1302 | C2 | semidirect |
| 7. #67750 | C2 | semidirect |
| 17. #4843 | C4 | semidirect |
| 18. #4843 | C4 | semidirect |
| 19. #4842 | C4 | semidirect |
| 20. #4842 | C4 | semidirect |
| 39. #1302 | D3 | semidirect |
| 432. C3 | #9163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79343 | 2 |
| #79287 | 2 |
| #70789 | 2 |
| #69812 | 2 |
| #69798 | 2 |
| C3×#1302 | 2 |
| #67750 | 2 |
| #9163 | 3 |