Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
3550 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 667 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 |
|---|---|---|
| 3. C2×#4947 | C2 | semidirect |
| 4. #73844 | C2 | direct (N × H) |
| 7. C23×Dic6 | C22 | semidirect |
| 12. C2×C3⋊#95 | C22 | semidirect |
| 13. #4947 | C22 | semidirect |
| 19. C25×C3 | Q8 | semidirect |
| 25. C22×Dic6 | C23 | semidirect |
| 30. C3⋊#95 | C23 | semidirect |
| 45. C24×C3 | C2×Q8 | semidirect |
| 57. C25 | Dic6 | semidirect |
| 92. C24 | C2×Dic6 | semidirect |
| 132. C2×C3 | #2840 | semidirect |
| 146. C3 | C2×#2840 | semidirect |
| 148. C2 | #73844 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#379 | 2 |
| C2×#5247 | 2 |
| C2×#4947 | 2 |
| #73844 | 2 |
| C2×#2840 | 3 |