Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
140 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 30 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 |
|---|---|---|
| 1. C22⋊#13095525 | C2 | semidirect |
| 20. C23×C97 | C16 | semidirect |
| 25. C22×D97 | C16 | semidirect |
| 62. C97 | #1314 | semidirect |
| 88. C23 | #13095525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊#13095525 | 2 |
| C2×C22⋊#11715906 | 2 |
| #1314 | 97 |