Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15692280 | C2 | semidirect |
| 2. C22×D808 | C2 | semidirect |
| 3. #20265741 | C2 | semidirect |
| 4. #20265651 | C2 | semidirect |
| 5. #20265395 | C2 | semidirect |
| 6. #20265371 | C2 | semidirect |
| 7. #20265203 | C2 | semidirect |
| 8. #20265181 | C2 | semidirect |
| 9. #416×C101 | C2 | semidirect |
| 13. C2×#13108061 | C22 | semidirect |
| 16. C2×#13108059 | C22 | semidirect |
| 18. #15692251 | C22 | semidirect |
| 19. #15692244 | C22 | semidirect |
| 23. #15692217 | C22 | semidirect |
| 26. #15692184 | C22 | semidirect |
| 27. #15692175 | C22 | semidirect |
| 31. #103×C101 | C22 | semidirect |
| 32. #102×C101 | C22 | semidirect |
| 40. C2×D404 | D4 | semidirect |
| 122. C101 | #3041 | semidirect |
| 131. #416 | D101 | semidirect |
| 152. #103 | C2×D101 | semidirect |
| 154. #102 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692280 | 2 |
| C22×D808 | 2 |
| #20265741 | 2 |
| #20265651 | 2 |
| #20265395 | 2 |
| #20265371 | 2 |
| #20265203 | 2 |
| #20265181 | 2 |
| #416×C101 | 2 |
| #3041 | 101 |