Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
180 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 7. #15690865 | C4 | semidirect |
| 12. #15690721 | C4 | semidirect |
| 14. #97×C97 | C4 | semidirect |
| 64. C97 | #1295 | semidirect |
| 76. #97 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261694 | 2 |
| #20261679 | 2 |
| #97×D97 | 2 |
| #1295 | 97 |