Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 8. #15690881 | C4 | semidirect |
| 9. #15690880 | C4 | semidirect |
| 10. #15690879 | C4 | semidirect |
| 11. #15690878 | C4 | semidirect |
| 17. C4×#11715895 | C4 | semidirect |
| 18. C8×Dic97 | C4 | semidirect |
| 19. C8×Dic97 | C4 | semidirect |
| 20. C4×C8×C97 | C4 | semidirect |
| 80. C97 | #1772 | semidirect |
| 100. C4×C8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#108 | 2 |
| #20261745 | 2 |
| #20261698 | 2 |
| #20261606 | 2 |
| C4×C8×D97 | 2 |
| #1772 | 97 |