Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#15692279 | C2 | semidirect |
| 2. #20265822 | C2 | semidirect |
| 3. #20265561 | C2 | semidirect |
| 4. #20265424 | C2 | semidirect |
| 5. #20265392 | C2 | semidirect |
| 6. #20265340 | C2 | semidirect |
| 7. #20265312 | C2 | semidirect |
| 8. #20265256 | C2 | semidirect |
| 9. C4×D8×C101 | C2 | semidirect |
| 11. C2×D4×D101 | C22 | semidirect |
| 13. C2×Dic404 | C22 | semidirect |
| 14. C2×#13108063 | C22 | semidirect |
| 15. C2×#13108062 | C22 | semidirect |
| 18. C2×#13108057 | C22 | semidirect |
| 19. #15692243 | C22 | semidirect |
| 21. #15692235 | C22 | semidirect |
| 27. C4⋊#11717579 | C22 | semidirect |
| 28. #15692178 | C22 | semidirect |
| 29. #15692175 | C22 | semidirect |
| 30. #15692167 | C22 | semidirect |
| 32. C4×D4×C101 | C22 | semidirect |
| 33. #107×C101 | C22 | semidirect |
| 34. #102×C101 | C22 | semidirect |
| 35. C4×C8×C101 | C22 | semidirect |
| 65. D8×C101 | D4 | semidirect |
| 125. C101 | #3273 | semidirect |
| 133. C4×D8 | D101 | semidirect |
| 152. C4×D4 | C2×D101 | semidirect |
| 154. #107 | C2×D101 | semidirect |
| 158. #102 | C2×D101 | semidirect |
| 160. C4×C8 | C2×D101 | semidirect |
| 181. D8 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692279 | 2 |
| #20265822 | 2 |
| #20265561 | 2 |
| #20265424 | 2 |
| #20265392 | 2 |
| #20265340 | 2 |
| #20265312 | 2 |
| #20265256 | 2 |
| C4×D8×C101 | 2 |
| #3273 | 101 |