Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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. #15690864 | C4 | semidirect |
| 9. C8×#87604 | C4 | semidirect |
| 13. #15690720 | C4 | semidirect |
| 14. C4×#11715895 | C4 | semidirect |
| 15. C8×Dic97 | C4 | semidirect |
| 16. #97×C97 | C4 | semidirect |
| 62. C97 | #1747 | semidirect |
| 75. #97 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261698 | 2 |
| #20261604 | 2 |
| #20261603 | 2 |
| #20261602 | 2 |
| #20260692 | 2 |
| #1747 | 97 |