Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1424 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 750 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. #20261814 | C2 | semidirect |
| 2. #20261813 | C2 | semidirect |
| 3. D97⋊#131 | C2 | semidirect |
| 4. C2×#15690897 | C2 | semidirect |
| 6. #15690898 | C22 | semidirect |
| 7. #15690898 | C22 | semidirect |
| 8. #15690897 | C22 | semidirect |
| 9. #15690897 | C22 | semidirect |
| 10. #15690897 | C22 | semidirect |
| 11. C2×#13095521 | C22 | semidirect |
| 12. D97⋊M16 | C22 | semidirect |
| 13. C2×#13095520 | C22 | semidirect |
| 14. C2×#13095519 | C22 | semidirect |
| 15. C22×#11715897 | C22 | semidirect |
| 67. C97 | #3573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261814 | 2 |
| #20261813 | 2 |
| D97⋊#131 | 2 |
| C2×#15690897 | 2 |
| #20261570 | 2 |
| #3573 | 97 |