Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
202 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 2. #20260490 | C2 | semidirect |
| 3. #336×C97 | C2 | semidirect |
| 15. C2×D388 | C8 | semidirect |
| 89. C97 | #1270 | semidirect |
| 92. #336 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260637 | 2 |
| #20260490 | 2 |
| #336×C97 | 2 |
| #1270 | 97 |