Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
594 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 123 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. C3×#1752 | C2 | semidirect |
| 3. #71970 | C2 | semidirect |
| 4. #69944 | C2 | semidirect |
| 5. #69456 | C2 | semidirect |
| 9. C22×D24 | C4 | semidirect |
| 18. C2×#821 | C4 | semidirect |
| 19. C2×#818 | C4 | semidirect |
| 28. #1752 | D3 | semidirect |
| 205. C3×C8 | #99 | semidirect |
| 316. C8 | #806 | semidirect |
| 347. C3 | #9785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5115 | 2 |
| C3×#1752 | 2 |
| #71970 | 2 |
| #69944 | 2 |
| #69456 | 2 |
| #9785 | 3 |