Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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. #20266244 | C2 | semidirect |
| 2. #20266218 | C2 | semidirect |
| 3. D8×#87938 | C2 | semidirect |
| 4. #20266187 | C2 | semidirect |
| 5. #20266169 | C2 | semidirect |
| 6. #20266140 | C2 | semidirect |
| 10. D4×#87938 | C22 | semidirect |
| 14. #15692324 | C22 | semidirect |
| 15. #15692323 | C22 | semidirect |
| 16. #15692317 | C22 | semidirect |
| 17. #15692309 | C22 | semidirect |
| 18. C8×#87938 | C22 | semidirect |
| 20. C2×D808 | C4 | semidirect |
| 21. C2×#13108059 | C4 | semidirect |
| 22. D8×D101 | C4 | semidirect |
| 23. D8×D101 | C4 | semidirect |
| 27. C2×D8×C101 | C4 | semidirect |
| 40. C2×D404 | C2×C4 | semidirect |
| 44. D4×D101 | C2×C4 | semidirect |
| 47. D808 | C2×C4 | semidirect |
| 48. D808 | C2×C4 | semidirect |
| 49. #13108059 | C2×C4 | semidirect |
| 50. #13108059 | C2×C4 | semidirect |
| 51. C2×#11717579 | C2×C4 | semidirect |
| 52. C8×D101 | C2×C4 | semidirect |
| 53. C8×D101 | C2×C4 | semidirect |
| 56. C2×D4×C101 | C2×C4 | semidirect |
| 57. D8×C101 | C2×C4 | semidirect |
| 58. D8×C101 | C2×C4 | semidirect |
| 59. C2×C8×C101 | C2×C4 | semidirect |
| 109. C101 | #2948 | semidirect |
| 124. C2×D8 | #87938 | semidirect |
| 144. C2×D4 | C2×#87938 | semidirect |
| 151. D8 | C2×#87938 | semidirect |
| 152. D8 | C2×#87938 | semidirect |
| 161. C2×C8 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266244 | 2 |
| #20266218 | 2 |
| D8×#87938 | 2 |
| #20266187 | 2 |
| #20266169 | 2 |
| #20266140 | 2 |
| C2×D8×D101 | 2 |
| #2948 | 101 |