Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
132 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 7. #15690883 | C4 | semidirect |
| 9. #15690878 | C4 | semidirect |
| 13. #15690742 | C4 | semidirect |
| 14. #106×C97 | C4 | semidirect |
| 60. C97 | #1384 | semidirect |
| 74. #106 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261791 | 2 |
| #20261745 | 2 |
| #20260770 | 2 |
| #1384 | 97 |