Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
248 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 21. #15690735 | C4 | semidirect |
| 22. #15690734 | C4 | semidirect |
| 23. #15690733 | C4 | semidirect |
| 24. #103×C97 | C4 | semidirect |
| 119. C97 | #1935 | semidirect |
| 139. #103 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690873 | 2 |
| C2×#15690864 | 2 |
| (C2×#87604)⋊Q8 | 2 |
| #20261686 | 2 |
| #20261609 | 2 |
| #20261608 | 2 |
| #103×D97 | 2 |
| #1935 | 97 |