Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
108 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 29 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 |
|---|---|---|
| 1. #20261830 | C2 | semidirect |
| 2. #20261824 | C2 | semidirect |
| 19. D776 | C8 | semidirect |
| 22. D8×C97 | C8 | semidirect |
| 52. C97 | #1333 | semidirect |
| 67. D8 | #11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261830 | 2 |
| #20261824 | 2 |
| D8×#87604 | 2 |
| #1333 | 97 |