Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
212 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 23. #101×C97 | C4 | semidirect |
| 94. C97 | #1930 | semidirect |
| 115. #101 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260777 | 2 |
| #20260744 | 2 |
| C2×#15690734 | 2 |
| #20260693 | 2 |
| #20260503 | 2 |
| #20260499 | 2 |
| C2×#101×C97 | 2 |
| #1930 | 97 |