Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 7. C4×#11715897 | C4 | semidirect |
| 11. #15690721 | C4 | semidirect |
| 12. #15690720 | C4 | semidirect |
| 13. #97×C97 | C4 | semidirect |
| 50. C97 | #1746 | semidirect |
| 61. #97 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095519 | 2 |
| #20261671 | 2 |
| #20261600 | 2 |
| #97×D97 | 2 |
| #1746 | 97 |