Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C22×Dic404 | C2 | semidirect |
| 4. C2×#15692220 | C2 | semidirect |
| 5. #20265398 | C2 | direct (N × H) |
| 6. C2×#15692184 | C2 | semidirect |
| 7. C2×#15692178 | C2 | semidirect |
| 12. C2×Dic404 | C22 | semidirect |
| 19. #15692220 | C22 | semidirect |
| 25. #15692184 | C22 | semidirect |
| 26. #15692178 | C22 | semidirect |
| 111. C2×C101 | #464 | semidirect |
| 116. C101 | C2×#464 | semidirect |
| 227. C2 | #20265398 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic404 | 2 |
| C22×#13108062 | 2 |
| C2×#15692242 | 2 |
| C2×#15692220 | 2 |
| #20265398 | 2 |
| C2×#15692184 | 2 |
| C2×#15692178 | 2 |
| C2×#102×C101 | 2 |
| C2×#464 | 101 |