Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20261502 | C2 | semidirect |
| 3. #20260753 | C2 | semidirect |
| 4. #20260701 | C2 | semidirect |
| 5. #20260505 | C2 | semidirect |
| 6. #20260500 | C2 | semidirect |
| 7. #416×C97 | C2 | semidirect |
| 10. #15690840 | C4 | semidirect |
| 12. #15690835 | C4 | semidirect |
| 119. C97 | #1881 | semidirect |
| 123. #416 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261533 | 2 |
| #20261502 | 2 |
| #20260753 | 2 |
| #20260701 | 2 |
| #20260505 | 2 |
| #20260500 | 2 |
| #416×C97 | 2 |
| #1881 | 97 |