Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×D8×D101 | C2 | semidirect |
| 2. #127×D101 | C2 | semidirect |
| 3. #20265554 | C2 | semidirect |
| 4. #20265553 | C2 | semidirect |
| 5. #20265552 | C2 | semidirect |
| 6. C4×C8×D101 | C2 | semidirect |
| 7. #493×C101 | C2 | semidirect |
| 10. C2×D808 | C22 | semidirect |
| 11. C2×#13108059 | C22 | semidirect |
| 14. #15692252 | C22 | semidirect |
| 16. #15692251 | C22 | semidirect |
| 18. C4×#11717579 | C22 | semidirect |
| 19. C8×Dic101 | C22 | semidirect |
| 20. C2×D8×C101 | C22 | semidirect |
| 21. #127×C101 | C22 | semidirect |
| 22. C4×C8×C101 | C22 | semidirect |
| 35. C8×D101 | D4 | semidirect |
| 58. C4×D101 | D8 | semidirect |
| 60. C8×C101 | C2×D4 | semidirect |
| 61. #11717579 | C2×D4 | semidirect |
| 70. C4×C101 | C2×D8 | semidirect |
| 73. Dic101 | C2×D8 | semidirect |
| 78. D101 | #493 | direct (N × H) |
| 80. C101 | C2×#493 | semidirect |
| 86. #493 | D101 | direct (N × H) |
| 93. C2×D8 | C2×D101 | semidirect |
| 98. #127 | C2×D101 | semidirect |
| 102. C4×C8 | C2×D101 | semidirect |
| 141. C8 | D4×D101 | semidirect |
| 152. C4 | D8×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D101 | 2 |
| #127×D101 | 2 |
| #20265554 | 2 |
| #20265553 | 2 |
| #20265552 | 2 |
| C4×C8×D101 | 2 |
| #493×C101 | 2 |
| C2×#493 | 101 |