Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
130 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 22. Dic388 | Q8 | semidirect |
| 60. C97 | #2227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261139 | 2 |
| #20260829 | 2 |
| #20260560 | 2 |
| #20260553 | 2 |
| #20260540 | 2 |
| #20260538 | 2 |
| #366×C97 | 2 |
| #2227 | 97 |