Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
170 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 27 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. #20261821 | C2 | semidirect |
| 15. C2×D388 | C8 | semidirect |
| 20. C2×D4×C97 | C8 | semidirect |
| 65. C97 | #1318 | semidirect |
| 78. C2×D4 | #11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261821 | 2 |
| #20261687 | 2 |
| #1318 | 97 |