Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 9. #15690880 | C4 | semidirect |
| 12. C8×#87604 | C4 | semidirect |
| 15. #15690743 | C4 | semidirect |
| 16. #15690742 | C4 | semidirect |
| 17. #106×C97 | C4 | semidirect |
| 69. C97 | #1772 | semidirect |
| 83. #106 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690880 | 2 |
| #20261700 | 2 |
| C2×C8×#87604 | 2 |
| #20261605 | 2 |
| #20260770 | 2 |
| #1772 | 97 |