Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #20265943 | C2 | semidirect |
| 3. #20265298 | C2 | semidirect |
| 4. #20265293 | C2 | semidirect |
| 5. C2×#15692181 | C2 | semidirect |
| 6. M16×Dic101 | C2 | semidirect |
| 7. #430×C101 | C2 | semidirect |
| 9. #15692288 | C4 | semidirect |
| 10. #15692283 | C4 | semidirect |
| 12. #15692263 | C22 | semidirect |
| 17. #15692181 | C22 | semidirect |
| 18. #15692181 | C22 | semidirect |
| 19. #15692165 | C22 | semidirect |
| 20. C8×Dic101 | C22 | semidirect |
| 23. #108×C101 | C22 | semidirect |
| 33. Dic404 | C2×C4 | semidirect |
| 34. #13108063 | C2×C4 | semidirect |
| 35. D808 | C2×C4 | semidirect |
| 86. C101 | #2956 | semidirect |
| 91. #430 | D101 | semidirect |
| 105. #108 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265977 | 2 |
| #20265943 | 2 |
| #20265298 | 2 |
| #20265293 | 2 |
| C2×#15692181 | 2 |
| M16×Dic101 | 2 |
| #430×C101 | 2 |
| #2956 | 101 |