Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#13108073 | C2 | semidirect |
| 2. C2×#15692276 | C2 | semidirect |
| 3. #20265690 | C2 | semidirect |
| 4. #20265336 | C2 | semidirect |
| 5. #20265332 | C2 | semidirect |
| 6. #20265323 | C2 | semidirect |
| 7. #20265318 | C2 | semidirect |
| 8. #20265311 | C2 | semidirect |
| 9. #20265170 | C2 | semidirect |
| 10. C22⋊C8×D101 | C2 | semidirect |
| 11. #450×C101 | C2 | semidirect |
| 12. C2×#13108075 | C22 | semidirect |
| 23. C2×#13108064 | C22 | semidirect |
| 24. C2×#13108063 | C22 | semidirect |
| 25. C2×#13108059 | C22 | semidirect |
| 26. C2×C8×D101 | C22 | semidirect |
| 28. #15692231 | C22 | semidirect |
| 29. #15692230 | C22 | semidirect |
| 34. #15692213 | C22 | semidirect |
| 35. #15692180 | C22 | semidirect |
| 36. #15692178 | C22 | semidirect |
| 37. #15692176 | C22 | semidirect |
| 39. #15692167 | C22 | semidirect |
| 41. C2×SD16×C101 | C22 | semidirect |
| 43. #102×C101 | C22 | semidirect |
| 52. #13108073 | D4 | semidirect |
| 147. C22×C101 | #135 | semidirect |
| 176. C101 | #3002 | semidirect |
| 182. #450 | D101 | semidirect |
| 202. C2×SD16 | C2×D101 | semidirect |
| 217. #102 | C2×D101 | semidirect |
| 333. C22 | #15692276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108073 | 2 |
| C2×#15692276 | 2 |
| #20265690 | 2 |
| #20265336 | 2 |
| #20265332 | 2 |
| #20265323 | 2 |
| #20265318 | 2 |
| #20265311 | 2 |
| #20265170 | 2 |
| C22⋊C8×D101 | 2 |
| #450×C101 | 2 |
| #3002 | 101 |