Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15692274 | C2 | semidirect |
| 2. C22×C8×D101 | C2 | semidirect |
| 3. #20265687 | C2 | semidirect |
| 4. #20265419 | C2 | semidirect |
| 5. #20265418 | C2 | semidirect |
| 6. #20265410 | C2 | semidirect |
| 7. #20265405 | C2 | semidirect |
| 8. #20265404 | C2 | semidirect |
| 9. #20265214 | C2 | semidirect |
| 10. #20265170 | C2 | semidirect |
| 11. #466×C101 | C2 | semidirect |
| 15. C2×Dic404 | C22 | semidirect |
| 16. C2×#13108062 | C22 | semidirect |
| 31. #15692189 | C22 | semidirect |
| 32. #15692186 | C22 | semidirect |
| 33. #15692180 | C22 | semidirect |
| 34. #15692178 | C22 | semidirect |
| 35. #15692176 | C22 | semidirect |
| 36. C2×D8×C101 | C22 | semidirect |
| 39. #107×C101 | C22 | semidirect |
| 40. #102×C101 | C22 | semidirect |
| 63. C8×D101 | D4 | semidirect |
| 121. C22×C101 | #135 | semidirect |
| 129. C2×D101 | #135 | semidirect |
| 146. C101 | #3050 | semidirect |
| 153. #466 | D101 | semidirect |
| 163. C2×D8 | C2×D101 | semidirect |
| 181. #107 | C2×D101 | semidirect |
| 186. #102 | C2×D101 | semidirect |
| 274. C22 | #15692274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692274 | 2 |
| C22×C8×D101 | 2 |
| #20265687 | 2 |
| #20265419 | 2 |
| #20265418 | 2 |
| #20265410 | 2 |
| #20265405 | 2 |
| #20265404 | 2 |
| #20265214 | 2 |
| #20265170 | 2 |
| #466×C101 | 2 |
| #3050 | 101 |