Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #20260744 | C2 | semidirect |
| 5. #20260505 | C2 | semidirect |
| 6. #20260491 | C2 | semidirect |
| 7. #519×C97 | C2 | semidirect |
| 11. C2×#13095501 | C4 | semidirect |
| 12. C2×#13095498 | C4 | semidirect |
| 110. C97 | #1905 | semidirect |
| 112. #519 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690841 | 2 |
| #20260753 | 2 |
| #20260744 | 2 |
| #20260708 | 2 |
| #20260505 | 2 |
| #20260491 | 2 |
| #519×C97 | 2 |
| #1905 | 97 |