Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
234 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 4. C23×#87604 | C4 | semidirect |
| 7. C2×C22⋊#87604 | C4 | semidirect |
| 9. #15690870 | C4 | semidirect |
| 13. #15690725 | C4 | semidirect |
| 15. #99×C97 | C4 | semidirect |
| 107. C97 | #1390 | semidirect |
| 121. #99 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#100 | 2 |
| #20261683 | 2 |
| #99×D97 | 2 |
| #1390 | 97 |