Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#15692303 | C2 | semidirect |
| 2. #20265977 | C2 | semidirect |
| 3. #20265751 | C2 | semidirect |
| 4. #20265362 | C2 | semidirect |
| 5. #20265352 | C2 | semidirect |
| 6. #20265193 | C2 | semidirect |
| 7. C2×#101×C101 | C2 | semidirect |
| 17. #15692288 | C22 | semidirect |
| 19. #15692283 | C22 | semidirect |
| 21. #15692253 | C22 | semidirect |
| 22. #15692244 | C22 | semidirect |
| 26. #15692181 | C22 | semidirect |
| 29. #101×C101 | C22 | semidirect |
| 124. C101 | #3020 | semidirect |
| 131. C2×#101 | D101 | semidirect |
| 153. #101 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692303 | 2 |
| #20265977 | 2 |
| #20265751 | 2 |
| #20265362 | 2 |
| #20265352 | 2 |
| #20265193 | 2 |
| C2×#101×C101 | 2 |
| #3020 | 101 |