Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265722 | C2 | semidirect |
| 2. C2×#15692217 | C2 | semidirect |
| 3. #20265490 | C2 | semidirect |
| 4. #20265456 | C2 | semidirect |
| 5. #20265371 | C2 | semidirect |
| 6. #20265313 | C2 | semidirect |
| 7. #20265310 | C2 | semidirect |
| 8. #20265259 | C2 | semidirect |
| 9. #20265257 | C2 | semidirect |
| 10. #20265227 | C2 | semidirect |
| 11. #480×C101 | C2 | semidirect |
| 17. #15692254 | C22 | semidirect |
| 18. #15692251 | C22 | semidirect |
| 22. D4×Dic101 | C22 | semidirect |
| 27. #15692217 | C22 | semidirect |
| 31. #15692188 | C22 | semidirect |
| 32. #15692184 | C22 | semidirect |
| 35. #15692175 | C22 | semidirect |
| 37. C8×Dic101 | C22 | semidirect |
| 40. #107×C101 | C22 | semidirect |
| 41. #102×C101 | C22 | semidirect |
| 104. C2×Dic101 | D8 | semidirect |
| 112. D404 | #41 | semidirect |
| 150. C101 | #3100 | semidirect |
| 154. #480 | D101 | semidirect |
| 184. #107 | C2×D101 | semidirect |
| 189. #102 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265722 | 2 |
| C2×#15692217 | 2 |
| #20265490 | 2 |
| #20265456 | 2 |
| #20265371 | 2 |
| #20265313 | 2 |
| #20265310 | 2 |
| #20265259 | 2 |
| #20265257 | 2 |
| #20265227 | 2 |
| #480×C101 | 2 |
| #3100 | 101 |