Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
296 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 9. C4×#11715897 | C4 | semidirect |
| 10. C4×#11715897 | C4 | semidirect |
| 13. C4×#11715895 | C4 | semidirect |
| 14. C8×Dic97 | C4 | semidirect |
| 15. C4×C8×C97 | C4 | semidirect |
| 21. C4×#87604 | C8 | semidirect |
| 64. C97 | #1744 | semidirect |
| 79. C4×C8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095519 | 2 |
| C42×#87604 | 2 |
| #20261600 | 2 |
| C4×C8×D97 | 2 |
| #1744 | 97 |