Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
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×#15690838 | C2 | semidirect |
| 2. C2×#15690830 | C2 | semidirect |
| 3. #20261299 | C2 | semidirect |
| 4. #20261216 | C2 | semidirect |
| 5. #20260960 | C2 | semidirect |
| 6. #20260953 | C2 | semidirect |
| 7. #20260934 | C2 | semidirect |
| 8. #20260929 | C2 | semidirect |
| 9. #20260763 | C2 | semidirect |
| 10. C2×#15690730 | C2 | semidirect |
| 11. #417×C97 | C2 | semidirect |
| 16. C2×#13095501 | C22 | semidirect |
| 18. C2×#13095499 | C22 | semidirect |
| 19. C2×#13095498 | C22 | semidirect |
| 21. C2×#13095496 | C22 | semidirect |
| 28. #15690775 | C22 | semidirect |
| 29. #15690772 | C22 | semidirect |
| 34. #15690739 | C22 | semidirect |
| 35. #15690739 | C22 | semidirect |
| 41. #103×C97 | C22 | semidirect |
| 42. #102×C97 | C22 | semidirect |
| 45. #13095511 | D4 | semidirect |
| 155. C97 | #3045 | semidirect |
| 165. #417 | D97 | semidirect |
| 194. #103 | C2×D97 | semidirect |
| 197. #102 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690838 | 2 |
| C2×#15690830 | 2 |
| #20261299 | 2 |
| #20261216 | 2 |
| #20260960 | 2 |
| #20260953 | 2 |
| #20260934 | 2 |
| #20260929 | 2 |
| #20260763 | 2 |
| C2×#15690730 | 2 |
| #417×C97 | 2 |
| #3045 | 97 |