Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261363 | C2 | semidirect |
| 3. #20261098 | C2 | semidirect |
| 4. #20261096 | C2 | semidirect |
| 5. #20261091 | C2 | semidirect |
| 6. #20261080 | C2 | semidirect |
| 7. #20260739 | C2 | semidirect |
| 8. #20260736 | C2 | semidirect |
| 9. C2×#15690732 | C2 | semidirect |
| 10. #20260690 | C2 | semidirect |
| 11. #416×C97 | C2 | semidirect |
| 15. #15690809 | C22 | semidirect |
| 18. #15690801 | C22 | semidirect |
| 26. #15690734 | C22 | semidirect |
| 29. #15690731 | C22 | semidirect |
| 32. #15690720 | C22 | semidirect |
| 33. C8×Dic97 | C22 | semidirect |
| 37. #103×C97 | C22 | semidirect |
| 38. #103×C97 | C22 | semidirect |
| 39. #102×C97 | C22 | semidirect |
| 40. #102×C97 | C22 | semidirect |
| 136. C97 | #3136 | semidirect |
| 145. #416 | D97 | semidirect |
| 166. #103 | C2×D97 | semidirect |
| 167. #103 | C2×D97 | semidirect |
| 173. #102 | C2×D97 | semidirect |
| 174. #102 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261363 | 2 |
| #20261299 | 2 |
| #20261098 | 2 |
| #20261096 | 2 |
| #20261091 | 2 |
| #20261080 | 2 |
| #20260739 | 2 |
| #20260736 | 2 |
| C2×#15690732 | 2 |
| #20260690 | 2 |
| #416×C97 | 2 |
| #3136 | 97 |