Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
140 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 6. #15690885 | C4 | semidirect |
| 9. #15690878 | C4 | semidirect |
| 12. #15690744 | C4 | semidirect |
| 14. #107×C97 | C4 | semidirect |
| 64. C97 | #1386 | semidirect |
| 75. #107 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690885 | 2 |
| C2×#15690878 | 2 |
| #20260772 | 2 |
| #1386 | 97 |