Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 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×#15690835 | C2 | semidirect |
| 2. C22×D776 | C2 | semidirect |
| 3. #20261299 | C2 | semidirect |
| 4. #20261209 | C2 | semidirect |
| 5. #20260953 | C2 | semidirect |
| 6. #20260929 | C2 | semidirect |
| 7. #20260761 | C2 | semidirect |
| 8. #20260739 | C2 | semidirect |
| 9. #416×C97 | C2 | semidirect |
| 13. C2×#13095498 | C22 | semidirect |
| 16. C2×#13095496 | C22 | semidirect |
| 18. #15690806 | C22 | semidirect |
| 19. #15690799 | C22 | semidirect |
| 23. #15690772 | C22 | semidirect |
| 26. #15690739 | C22 | semidirect |
| 27. #15690730 | C22 | semidirect |
| 31. #103×C97 | C22 | semidirect |
| 32. #102×C97 | C22 | semidirect |
| 40. C2×D388 | D4 | semidirect |
| 122. C97 | #3041 | semidirect |
| 131. #416 | D97 | semidirect |
| 152. #103 | C2×D97 | semidirect |
| 154. #102 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690835 | 2 |
| C22×D776 | 2 |
| #20261299 | 2 |
| #20261209 | 2 |
| #20260953 | 2 |
| #20260929 | 2 |
| #20260761 | 2 |
| #20260739 | 2 |
| #416×C97 | 2 |
| #3041 | 97 |