Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×D404 | C2 | semidirect |
| 2. C2×#15692283 | C2 | semidirect |
| 3. #20265688 | C2 | semidirect |
| 4. #20265330 | C2 | semidirect |
| 5. #20265313 | C2 | semidirect |
| 6. #20265183 | C2 | semidirect |
| 7. #407×C101 | C2 | semidirect |
| 9. C2×#13108074 | C22 | semidirect |
| 16. C2×#13108063 | C22 | semidirect |
| 17. C2×D808 | C22 | semidirect |
| 19. #15692234 | C22 | semidirect |
| 20. #15692229 | C22 | semidirect |
| 23. #15692214 | C22 | semidirect |
| 24. #15692177 | C22 | semidirect |
| 26. C2×M16×C101 | C22 | semidirect |
| 27. C22⋊C8×C101 | C22 | semidirect |
| 33. C2×Dic202 | C23 | semidirect |
| 40. C2×D404 | D4 | semidirect |
| 42. C2×D404 | C23 | semidirect |
| 48. C4⋊Dic101 | C23 | semidirect |
| 61. C2×C8×C101 | C23 | semidirect |
| 98. C22×C101 | AGL(1,ℤ/8) | semidirect |
| 118. C101 | #3003 | semidirect |
| 125. #407 | D101 | semidirect |
| 137. C2×M16 | C2×D101 | semidirect |
| 145. C22⋊C8 | C2×D101 | semidirect |
| 173. C2×C8 | C22×D101 | semidirect |
| 222. C22 | #15692283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D404 | 2 |
| C2×#15692283 | 2 |
| #20265688 | 2 |
| #20265330 | 2 |
| #20265313 | 2 |
| #20265183 | 2 |
| #407×C101 | 2 |
| #3003 | 101 |