Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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×#15692283 | C2 | semidirect |
| 2. C2×#15692275 | C2 | semidirect |
| 3. #20265741 | C2 | semidirect |
| 4. #20265658 | C2 | semidirect |
| 5. #20265402 | C2 | semidirect |
| 6. #20265395 | C2 | semidirect |
| 7. #20265376 | C2 | semidirect |
| 8. #20265371 | C2 | semidirect |
| 9. #20265205 | C2 | semidirect |
| 10. C2×#15692175 | C2 | semidirect |
| 11. #417×C101 | C2 | semidirect |
| 16. C2×#13108064 | C22 | semidirect |
| 18. C2×#13108062 | C22 | semidirect |
| 19. C2×#13108061 | C22 | semidirect |
| 21. C2×#13108059 | C22 | semidirect |
| 28. #15692220 | C22 | semidirect |
| 29. #15692217 | C22 | semidirect |
| 34. #15692184 | C22 | semidirect |
| 35. #15692184 | C22 | semidirect |
| 41. #103×C101 | C22 | semidirect |
| 42. #102×C101 | C22 | semidirect |
| 45. #13108074 | D4 | semidirect |
| 155. C101 | #3045 | semidirect |
| 165. #417 | D101 | semidirect |
| 194. #103 | C2×D101 | semidirect |
| 197. #102 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692283 | 2 |
| C2×#15692275 | 2 |
| #20265741 | 2 |
| #20265658 | 2 |
| #20265402 | 2 |
| #20265395 | 2 |
| #20265376 | 2 |
| #20265371 | 2 |
| #20265205 | 2 |
| C2×#15692175 | 2 |
| #417×C101 | 2 |
| #3045 | 101 |