Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20265888 | C2 | semidirect |
| 3. #20265494 | C2 | semidirect |
| 4. #20265464 | C2 | semidirect |
| 5. #20265405 | C2 | semidirect |
| 6. #20265374 | C2 | semidirect |
| 7. #20265329 | C2 | semidirect |
| 8. C4×#13108063 | C2 | semidirect |
| 9. C8×D404 | C2 | semidirect |
| 10. #102×D101 | C2 | semidirect |
| 11. #486×C101 | C2 | semidirect |
| 15. C2×#13108062 | C22 | semidirect |
| 16. C2×C8×D101 | C22 | semidirect |
| 18. #15692235 | C22 | semidirect |
| 23. C4×Dic202 | C22 | semidirect |
| 27. C4⋊C4×D101 | C22 | semidirect |
| 28. #15692187 | C22 | semidirect |
| 29. #15692186 | C22 | semidirect |
| 30. C4⋊#11717579 | C22 | semidirect |
| 31. #15692180 | C22 | semidirect |
| 33. #15692176 | C22 | semidirect |
| 35. #15692167 | C22 | semidirect |
| 36. C4⋊Q8×C101 | C22 | semidirect |
| 38. #102×C101 | C22 | semidirect |
| 39. #102×C101 | C22 | semidirect |
| 40. C4×C8×C101 | C22 | semidirect |
| 99. D404 | SD16 | semidirect |
| 137. C101 | #3295 | semidirect |
| 140. #486 | D101 | semidirect |
| 154. C4⋊Q8 | C2×D101 | semidirect |
| 174. #102 | C2×D101 | semidirect |
| 175. #102 | C2×D101 | semidirect |
| 177. C4×C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265888 | 2 |
| #20265812 | 2 |
| #20265494 | 2 |
| #20265464 | 2 |
| #20265405 | 2 |
| #20265374 | 2 |
| #20265329 | 2 |
| C4×#13108063 | 2 |
| C8×D404 | 2 |
| #102×D101 | 2 |
| #486×C101 | 2 |
| #3295 | 101 |