Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
852 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 138 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. C2×#15690867 | C2 | semidirect |
| 2. C2×C22⋊#11715897 | C2 | semidirect |
| 4. C22×#11715897 | C22 | semidirect |
| 20. C23×D97 | C8 | semidirect |
| 71. C22×C97 | C22⋊C8 | semidirect |
| 84. C2×D97 | C22⋊C8 | semidirect |
| 96. C97 | #1779 | semidirect |
| 175. C22 | #15690867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690867 | 2 |
| C2×C22⋊#11715897 | 2 |
| C23×C4×D97 | 2 |
| #1779 | 97 |