Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×C8×D101 | C2 | semidirect |
| 3. C2×#15692213 | C2 | semidirect |
| 4. #20265170 | C2 | direct (N × H) |
| 5. C2×#15692180 | C2 | semidirect |
| 6. C2×#15692178 | C2 | semidirect |
| 7. C2×#15692176 | C2 | semidirect |
| 8. C2×#102×C101 | C2 | semidirect |
| 11. C2×#13108073 | C4 | semidirect |
| 19. C2×C8×D101 | C22 | semidirect |
| 21. #15692213 | C22 | semidirect |
| 25. #15692180 | C22 | semidirect |
| 26. #15692178 | C22 | semidirect |
| 27. #15692176 | C22 | semidirect |
| 31. #102×C101 | C22 | semidirect |
| 35. #13108073 | C2×C4 | semidirect |
| 123. C2×C101 | #416 | semidirect |
| 129. C101 | C2×#416 | semidirect |
| 137. C2×#102 | D101 | semidirect |
| 160. #102 | C2×D101 | semidirect |
| 253. C2 | #20265170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108073 | 2 |
| C22×C8×D101 | 2 |
| C2×#15692213 | 2 |
| #20265170 | 2 |
| C2×#15692180 | 2 |
| C2×#15692178 | 2 |
| C2×#15692176 | 2 |
| C2×#102×C101 | 2 |
| C2×#416 | 101 |